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this is election No. 15 of M2 3

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2 electromagnetic field period

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today

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we will study properties of materials and connection

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and connection currents

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this will cover your section 5.12

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5.4 of textbook

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this is academic week No. 8 of your semester

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the learning objectives of today's lecture would be

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to understand properties of different materials

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so that we can study the electric field

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propagation in that material space

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and to understand what is convection

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in conduction terms

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first of all the introduction in chapter No. 4

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the electrostatic fuse in free space over considered

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this chapter will cover electric

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electric fields in different types of materials

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so materials are generally classified as conductors

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and non conductors non

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conducting materials

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are usually referred as insulators

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or dialectrics

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so materials can be classified in terms of their

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conductivity that is Sigma

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and it is mailed in the Zuno SAU Mohos per meter

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or most more commonly it is siemens per meter

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now I will discuss properties of materials

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and how they are classified

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based upon this thing

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so the most important property is conductivity

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that is used for their classification

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a material with high conductivity that is a Sigma

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is very very greater than 1 is referred as metals

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so remember this thing

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and a material with small conductivity means very

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very smaller than 1

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is referred to as insulator or a dialector

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and the materials

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whose conductivity lies between those of metals

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and insulators are known as semiconductors

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the examples are at as following

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so in the metals we know that

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the most famous metals with higher conductivity are

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coppernant and ammonium

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and uh for the semiconductors

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we know these are a silicone and germanium

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and for the insulators or dialectics

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the most common Artie glasson or rubber insulators

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some conductors exhibit infinite conductivity

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at temperatures at temperature near to absolute zero

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so that is zero calorie and they are called

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they are called the superconductors

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the most common examples are aluminium

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and let the light like

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dielectric materials

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have a few electrons available for productions

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whereas the metals have abundance of free electrons

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so that their production is higher

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as I mention in the previous slide that the materials

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they are classified based upon their conductivity

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and if we start from the high conductivity materials

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so that is the example of your conductors right

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so in this particular case

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the materials

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conductivity has been layered at 20 degrees Celsius

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temperature and at a low frequencies

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so in that particular case under these conditions

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these are the conductivity of silver

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copper and gold and aluminium

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you can see here the silver is having the highest uh

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connectivity in this particular case

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and then once we move down in the in between region

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then that is your silicone and germinium

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that is your semiconductor dialect

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semiconductor materials

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and once we move towards the insulators or dialectrics

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so that you can see here the uh productivity is in the

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it is in the range of here

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um uh

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uh part of 10 rays from minus 4 and micros and uh

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PICO and uh your

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but you can see here the different nano and nano nano

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nano the semens per meter

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so if we see

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the conductivity

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depends upon frequency and temperature

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so these are the two things

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so conductivity is

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the increases with decrease in temperature

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because of what's to decrease the temperature

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the collision between free electrons

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disease reviews and once you increase the temperature

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the collision increases

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so with the reduction of temperature

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the conduct beauty is going to increase

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so as we reduce the temperature up to

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you can see that a zero gallon

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then is that those type of conductors

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the exhibit B superconductivity properties

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or know if it's study

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what is correction and conduction currents

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and what is

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difference between these two types of currents

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so electric current

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in general is caused by the motion of free electrons

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this is the convention current

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so current in empires

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the two are given area is the electric charges

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electric charges passing through that area

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per unit time

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so it is the rate of change of charges per unit time

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so that is the definition we must be therefore to

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once we talk about the current

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so it is the rate of change of current

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rate of change of charges

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passing through a certain circuit area

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so in a in a current of 1 mpair

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charge is being transferred

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at a rate of 1 column per second

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so this is the your basic definition

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so if current a Dell

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at the differential

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current Dell I flows to a plainer surface

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differential surface area of a Dell s

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then we define a technology

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that is known as the surface current density

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so it is the rate of this

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this you can see that current passing through

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current flowing through up Linar surface

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for the differential case

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it is the Dell I divided by that Dell s

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so it is the number of lines

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you can see

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that number of lines cutting through that surface area

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or the

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or the current passing to a surface area of that

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as in this case so if

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if these two currents

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if these two parameters that is your a J

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the current density and your differential surface area

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they are normal to each other

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you know that for surface area

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will consider the normal in this direction

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so if the direction of normal that is your N right

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so for example it is your L s and is your

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and then your G it is also passing by cutting

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cutting this surface like this one

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then uh since it is considered as a dot product

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so for in this particle case

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the angle between this G and this normal to surface

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it is it is equal to 0 degree right

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so calls of 0 will know that it is equal to 1

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so that's why it is the maximum current ones d er

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once your er er this current density

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it is making an an angle of er 0 degree

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which is back to surface normal

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and if the current it is not normal to the surface

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then we involve this

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a dot product between these two quantities

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so if we want to find out the total current

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finding of flowing to a certain surface

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so what we need to do

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we need to simply integrate this dot product over that

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anti surface so that is your um

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generalized definition for the current

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for non uniform areas so

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it is the surface integral of your dark product

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of this condensity surface condensity

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with respect to that differential surface area

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what is that convection card

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convection card does not involve conductors okay

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and consequently does not verify the own slot

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and occurs when the current flow flows through

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an insulating material or insulating

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insulating medium for example liquid gas vacuums

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so uh the example is like so these are the medium

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so the example is like

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you must have seen that electron

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electrons beam is passing through a vacuum 2

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so this is the basic example

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in this case no conduction is involved

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and directly the electron beam is uh

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uh passing through that vacuum 2

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anti claw electron beam

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it is bombard from the one end of the tube

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and it is received on the second end

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and we will see one of the example

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one of the experiment in our lab as well

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in which the we will project this electron beam on the

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on some surface to see as

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to see how it is emanating from the source

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and how it is collecting at the destination point

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so in this in this gate

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you can consider like this

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that there is a floor charge

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floor charge of density Roe v

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so it is a volume charge density and these

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these

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you can consider it is composed of these electrons

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so if they are moving at a velocity of you

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so if in this particular example your view

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it is directed along y axis for this

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this is unit access will be your a y

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and it is only having

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going to have the y component in this case

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now we define now what is the differential current

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uh in this particular case or what that case we

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we consider for example this area right

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this differential area in this case for this 3D uh

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cubic ball ball

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you can say it okay

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so what is a dalcu

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that you will know that it is a product of your volume

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chart density into the differential volume

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so as you okay

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let me highlight like this

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so for example it is your differential volume right

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this is your differential volume dial B

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this upper surface it is your dial s right

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or any side you can see this side

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you can better treat it like this

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because it is cutting your direction of electron B

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in this case than the we know from

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from our previous match that the charge

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it is the product of your charge density

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multiply by that differentiate volume

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so involve this definition further the volume

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it is the product of your differential surface area and

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and the third element third side

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so in this case we have taken dial s like this one

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the top one right

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and this we have taken the length like this one

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like this one okay

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so you can take okay

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no yes

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you can you don't take it right

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just take this one yes take

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this one to take this one right

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and take this land so that we can complete a

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complete a volume in this case

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and then tell us

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is obviously cutting the direction of electronbeam in

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which would all teach you why

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okay then uh

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involve the definition of your velocity

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we know that it is the

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it is the rate of change of your distance so it

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so in this rate of change of speed

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rate of change of distance

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and if it is a in one part of your direction

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then it is known as your velocity

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okay so you must remember that B is equal to s by t

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yeah B is equal to s by t

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so in this particular example

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the s is equal to L y

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and the differential time is that t

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okay so that is your velocity is your Y

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okay not involve the definitions

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definitions of gy gy

261

00:11:51,733  -->  00:11:53,133
it is we know that

262

00:11:53,133  -->  00:11:55,300
it is the ratio of the current

263

00:11:55,300  -->  00:11:56,700
passing to that differential area

264

00:11:56,700  -->  00:11:59,166
so it is the ratio of the life or what the s

265

00:11:59,366  -->  00:12:02,566
and from here we plug in the value of del I

266

00:12:02,566  -->  00:12:04,100
so plug in plug this

267

00:12:04,100  -->  00:12:05,700
plug in value plug

268

00:12:05,700  -->  00:12:06,766
plug in this value

269

00:12:06,766  -->  00:12:11,300
then this Del s is going to get crossed with Del s

270

00:12:11,300  -->  00:12:13,033
and we are only left with this one

271

00:12:13,100  -->  00:12:16,466
so in general so in general it is only for y companies

272

00:12:16,466  -->  00:12:20,366
so in general your G is the product of

273

00:12:20,366  -->  00:12:22,166
for the correction grant I'm talking about

274

00:12:22,166  -->  00:12:25,433
so G is the product of your volume chart density

275

00:12:25,533  -->  00:12:28,533
and the velocity with which the current

276

00:12:28,533  -->  00:12:30,366
sun moving along one particular

277

00:12:30,366  -->  00:12:33,133
or around the 3 3 d uh

278

00:12:33,133  -->  00:12:35,566
3 direction if it is a 3D current

279

00:12:35,566  -->  00:12:37,800
so this is take away from this line

280

00:12:39,500  -->  00:12:41,033
what is the conduction current

281

00:12:41,166  -->  00:12:43,566
conduction current requires a conductor

282

00:12:43,566  -->  00:12:45,333
so so correction conduction current

283

00:12:45,333  -->  00:12:47,700
it is for insulator and conduction current

284

00:12:47,700  -->  00:12:50,000
it is for conductors so conductors

285

00:12:50,000  -->  00:12:52,566
a conductor has a large number of electrons

286

00:12:52,566  -->  00:12:55,000
that provide conduction current

287

00:12:55,000  -->  00:12:57,500
due to an impressed electric field

288

00:12:57,500  -->  00:13:00,266
so once an electric field is applied

289

00:13:00,266  -->  00:13:05,133
then the then the flow of free electrons starts right

290

00:13:05,133  -->  00:13:06,166
so conduction current

291

00:13:06,166  -->  00:13:07,733
has a large number of free electrons

292

00:13:07,733  -->  00:13:10,433
No. 1 and that provides the conduction current

293

00:13:10,533  -->  00:13:14,000
once an external electric release being applied

294

00:13:14,000  -->  00:13:15,333
so you can take it like E

295

00:13:15,333  -->  00:13:19,166
E right and when electric red is applied

296

00:13:19,166  -->  00:13:21,966
we know that from our previous lectures

297

00:13:21,966  -->  00:13:22,900
that force on a

298

00:13:22,900  -->  00:13:26,133
on a one electron it is so F is equal to Q e

299

00:13:26,133  -->  00:13:27,900
remember this thing the Coolens law

300

00:13:30,200  -->  00:13:33,466
right so in this case your q is minus E

301

00:13:33,466  -->  00:13:36,366
the electron and E is the electrocule intensity

302

00:13:36,566  -->  00:13:37,933
so in free space

303

00:13:37,933  -->  00:13:40,766
the electron would accelerate under the uh

304

00:13:40,766  -->  00:13:43,500
under the influence of this external electric feed

305

00:13:43,500  -->  00:13:45,100
in materials uh

306

00:13:45,100  -->  00:13:46,100
in different materials

307

00:13:46,100  -->  00:13:49,566
the electron suffers a continual collision

308

00:13:49,566  -->  00:13:50,600
and you remember that

309

00:13:50,600  -->  00:13:53,500
that collision is known as the Brownian motion

310

00:13:53,666  -->  00:13:55,500
in general as well so

311

00:13:55,500  -->  00:13:57,800
the electron will move with a different

312

00:13:57,800  -->  00:13:59,533
rusties between collision

313

00:13:59,533  -->  00:14:00,400
and they will collide

314

00:14:00,400  -->  00:14:03,166
so that's why we say that once the

315

00:14:03,400  -->  00:14:05,900
once there is a high temperature then the

316

00:14:05,900  -->  00:14:07,466
the collision is more so

317

00:14:07,466  -->  00:14:07,933
that's why

318

00:14:07,933  -->  00:14:11,400
the distivity of that material is going to increase

319

00:14:15,333  -->  00:14:17,366
let's further generalize this thing

320

00:14:17,533  -->  00:14:19,766
the average velocity for this

321

00:14:21,133  -->  00:14:23,866
random motion of electrons

322

00:14:23,866  -->  00:14:26,566
under the impact of the collision

323

00:14:26,566  -->  00:14:29,333
and under the influence of external electric field

324

00:14:29,333  -->  00:14:31,566
is known as the drift velocity

325

00:14:31,566  -->  00:14:32,566
the average velocity

326

00:14:32,733  -->  00:14:35,733
so every change in the momentum of free electron

327

00:14:35,733  -->  00:14:38,433
for example single electron E must

328

00:14:38,500  -->  00:14:40,266
must match the applied force

329

00:14:40,300  -->  00:14:43,333
now here we are making use of neutrons

330

00:14:43,333  -->  00:14:44,266
two laws the

331

00:14:44,266  -->  00:14:46,366
here it is the a physical m

332

00:14:46,366  -->  00:14:48,066
a the second law of neutrons

333

00:14:48,100  -->  00:14:49,700
so we know that the mass is m

334

00:14:49,700  -->  00:14:53,066
and we know that the acceleration of your electron

335

00:14:53,066  -->  00:14:56,066
it is the drift we lost you with respect to Tao

336

00:14:56,166  -->  00:14:58,566
Tao we know that it is the rate of acceleration

337

00:14:58,566  -->  00:15:01,233
it is the rate of change of year and we lost it

338

00:15:01,366  -->  00:15:04,766
and then we create this thing using the nutrients

339

00:15:04,766  -->  00:15:06,800
3rd law that is year

340

00:15:07,733  -->  00:15:08,966
you think that

341

00:15:08,966  -->  00:15:12,933
so from here you can equate this coolants law

342

00:15:12,933  -->  00:15:16,300
force being exerted on the electrons

343

00:15:16,300  -->  00:15:18,200
under the influence of external field

344

00:15:18,300  -->  00:15:20,266
and then you can equate these two

345

00:15:21,100  -->  00:15:24,866
under the impact of Newton's third law right third law

346

00:15:28,266  -->  00:15:29,866
and this was your 2nd law

347

00:15:31,500  -->  00:15:33,166
nutrients right

348

00:15:34,766  -->  00:15:38,300
okay and then if you play around these things

349

00:15:38,300  -->  00:15:40,266
so from here you can extract this thing

350

00:15:40,266  -->  00:15:43,166
the drift velocity so here Tao is the average

351

00:15:43,166  -->  00:15:45,100
because we're being the drift velocity

352

00:15:45,100  -->  00:15:45,800
which is known as

353

00:15:45,800  -->  00:15:48,166
the average velocity of the urban electron

354

00:15:48,166  -->  00:15:50,500
under the different collisions

355

00:15:50,500  -->  00:15:54,166
and under the backducture applied force due to a

356

00:15:54,166  -->  00:15:55,833
due to external electric field

357

00:15:55,866  -->  00:15:59,000
so Tao is the average time between the collision

358

00:15:59,266  -->  00:16:03,333
m is the mass of uh electron and drift lostee

359

00:16:03,333  -->  00:16:03,866
here you know

360

00:16:03,866  -->  00:16:04,566
the here

361

00:16:04,566  -->  00:16:05,600
observed that the drift

362

00:16:05,600  -->  00:16:08,700
lostee is directly proportional to the applied field

363

00:16:08,700  -->  00:16:11,300
that is your electric field intensity

364

00:16:12,733  -->  00:16:12,900
now

365

00:16:12,900  -->  00:16:15,733
if there are any number of electrons per unit volume

366

00:16:15,733  -->  00:16:18,933
then we can define that it's volume charge density

367

00:16:18,933  -->  00:16:20,566
it is the product of your charge

368

00:16:20,566  -->  00:16:22,100
times number of electrons

369

00:16:22,100  -->  00:16:24,366
so since it is a minus e charge

370

00:16:24,366  -->  00:16:28,400
so it is minus and e the connection current is er

371

00:16:28,500  -->  00:16:31,466
er J now Jay Z Pertudrovi

372

00:16:31,933  -->  00:16:34,000
that is your volume volume

373

00:16:34,800  -->  00:16:36,933
volume chart density times d drift

374

00:16:36,933  -->  00:16:38,600
lost it so here

375

00:16:38,600  -->  00:16:40,100
the difference here we have the

376

00:16:41,133  -->  00:16:43,666
uh drift last year uh

377

00:16:43,666  -->  00:16:44,700
for under the

378

00:16:44,700  -->  00:16:48,466
under the influence of external feed and previously uh

379

00:16:48,466  -->  00:16:49,766
in the convection current

380

00:16:49,766  -->  00:16:51,933
this we lost was the we lost it which

381

00:16:51,933  -->  00:16:52,366
which uh

382

00:16:52,366  -->  00:16:56,366
with which the electron beam was bombard in the vacuum

383

00:16:56,366  -->  00:16:57,166
two

384

00:16:57,933  -->  00:16:59,300
now put this uh uh

385

00:16:59,300  -->  00:17:01,300
Gypsy from here uh

386

00:17:01,300  -->  00:17:04,000
simplify this equation so how uh uh

387

00:17:04,000  -->  00:17:07,133
simplify this equation like this that you

388

00:17:07,133  -->  00:17:08,966
you know that from Baum's Law

389

00:17:09,133  -->  00:17:10,566
okay let's simplify this

390

00:17:10,933  -->  00:17:12,733
you know uh uh

391

00:17:12,733  -->  00:17:15,600
put this thing so let's define a technology over here

392

00:17:15,600  -->  00:17:17,000
so this thing right

393

00:17:17,000  -->  00:17:18,400
so this thing is known as

394

00:17:18,400  -->  00:17:21,500
the conductivity of that material

395

00:17:21,500  -->  00:17:22,533
the conductor right

396

00:17:22,533  -->  00:17:23,566
we have defined this thing

397

00:17:23,566  -->  00:17:26,733
as a conductivity of material and uh uh

398

00:17:26,733  -->  00:17:28,400
based upon this this is the

399

00:17:29,466  -->  00:17:32,400
this is the new version of Homslaugh that you

400

00:17:32,400  -->  00:17:33,966
that you have seen for the uh

401

00:17:33,966  -->  00:17:36,333
previous days you have seen BJ go to IR

402

00:17:36,333  -->  00:17:37,400
but for this uh

403

00:17:37,400  -->  00:17:38,866
under the impact of uh

404

00:17:39,333  -->  00:17:41,966
electric feed and the impact of electric feed

405

00:17:41,966  -->  00:17:44,966
and using the definition of its conductivity

406

00:17:44,966  -->  00:17:45,400
the eh

407

00:17:45,400  -->  00:17:47,300
we have dried another eh

408

00:17:47,300  -->  00:17:50,266
form of orms now that is Jade equal to Sigma E

409

00:17:53,066  -->  00:17:54,533
no a conductor has

410

00:17:54,533  -->  00:17:57,400
we know that a conductor has abundance of charge

411

00:17:57,400  -->  00:17:59,600
that is free to move right

412

00:17:59,600  -->  00:18:02,366
so a perfect conductor cannot

413

00:18:02,366  -->  00:18:06,600
contain an electrostatic field within it right

414

00:18:06,600  -->  00:18:10,200
otherwise the presence of electric fuel inside

415

00:18:10,200  -->  00:18:13,400
would not let charges to move freely

416

00:18:13,400  -->  00:18:15,366
so there will be a binding

417

00:18:15,400  -->  00:18:17,566
so next and there's consider keys

418

00:18:17,666  -->  00:18:20,900
consider keys like this so this is your original

419

00:18:20,933  -->  00:18:23,200
this is your original conductor right

420

00:18:23,200  -->  00:18:24,000
it is having a

421

00:18:24,000  -->  00:18:27,133
ample of electrons and it's having high conductivity

422

00:18:27,133  -->  00:18:30,633
so what happens that once electric field is being uh

423

00:18:30,966  -->  00:18:32,166
applied the external

424

00:18:32,300  -->  00:18:34,666
this external E E is external electric field e

425

00:18:34,666  -->  00:18:36,366
I is the internal electric field

426

00:18:36,666  -->  00:18:38,800
so they once the electric field is applied

427

00:18:38,800  -->  00:18:39,733
the electrons

428

00:18:39,733  -->  00:18:43,466
they align themselves in the direction of external

429

00:18:44,000  -->  00:18:46,600
the positive charges the positive positive

430

00:18:46,600  -->  00:18:48,366
you can see the positive charges

431

00:18:48,366  -->  00:18:50,033
they move in this direction

432

00:18:50,466  -->  00:18:54,000
the negative charges they move in this direction right

433

00:18:54,333  -->  00:18:56,133
so the natural that is like this

434

00:18:56,133  -->  00:18:59,900
under the impact of this external feel external E

435

00:18:59,933  -->  00:19:03,333
so first of all a lot of number of electrons

436

00:19:03,333  -->  00:19:05,700
so electrons move in the opposite direction

437

00:19:05,700  -->  00:19:09,166
electrons move in the uh in the direction of uh

438

00:19:10,200  -->  00:19:12,633
your electric field and uh

439

00:19:12,766  -->  00:19:14,100
cannot contain electroceiving

440

00:19:14,100  -->  00:19:16,466
so otherwise the presence of E field

441

00:19:16,466  -->  00:19:18,200
if there's a uh E field then

442

00:19:18,200  -->  00:19:20,766
if you're not allowing free motion of the electrons

443

00:19:20,766  -->  00:19:21,700
inside this

444

00:19:21,800  -->  00:19:24,300
so under the impact of external electric feed

445

00:19:24,300  -->  00:19:26,166
the positive charges move to where

446

00:19:26,166  -->  00:19:28,700
it moves in the direction of external electric feed

447

00:19:28,700  -->  00:19:30,666
and negative charges move in the direction

448

00:19:30,666  -->  00:19:32,033
in the opposite direction

449

00:19:32,333  -->  00:19:35,000
so now for this isolated conductor

450

00:19:35,000  -->  00:19:36,466
the natural zone is here

451

00:19:36,466  -->  00:19:40,700
there's no internal no internal lecture feel enhanced

452

00:19:40,700  -->  00:19:43,066
no internal uh surface uh

453

00:19:43,066  -->  00:19:46,500
volume chart density piled up inside the conductor

454

00:19:47,466  -->  00:19:50,000
and also you can relate it in this way

455

00:19:50,000  -->  00:19:52,100
that since the conductors

456

00:19:52,100  -->  00:19:54,766
they are having very very high conductivity

457

00:19:54,766  -->  00:19:58,800
so we we can see that from this forms

458

00:19:58,800  -->  00:20:02,233
law is equal to J divide by Sigma right

459

00:20:02,900  -->  00:20:06,433
so anything anything divided by infinity

460

00:20:06,766  -->  00:20:09,333
infinity is equal to zero

461

00:20:09,333  -->  00:20:10,066
so from here

462

00:20:10,066  -->  00:20:14,000
we can also into that the electric grid inside the

463

00:20:14,066  -->  00:20:16,600
but fact conductor is going to zero

464

00:20:17,400  -->  00:20:19,333
and in this essential

465

00:20:19,333  -->  00:20:22,100
will maintain a finite condensity

466

00:20:22,166  -->  00:20:26,000
and definitely if there's a other than conductivity

467

00:20:26,000  -->  00:20:28,466
then we will have a finite condensity

468

00:20:28,700  -->  00:20:29,566
so in this case

469

00:20:29,566  -->  00:20:32,200
we are going to have in finite condensity

470

00:20:33,500  -->  00:20:34,300
okay

471

00:20:34,966  -->  00:20:35,300
so

472

00:20:35,300  -->  00:20:39,333
based upon the previous assumptions inside conductor

473

00:20:39,333  -->  00:20:41,233
the es go es equal to zero

474

00:20:41,266  -->  00:20:43,466
and so we are talking about an isolated

475

00:20:43,466  -->  00:20:47,533
isolated a conductor and using this step in

476

00:20:47,533  -->  00:20:50,000
the relationship between electric and the

477

00:20:51,500  -->  00:20:53,466
electric feed and the electric potential

478

00:20:54,733  -->  00:20:58,100
so we know that is equal to tell me right

479

00:20:58,100  -->  00:21:00,400
so if you're is equal to zero

480

00:21:00,933  -->  00:21:03,266
then your value is your phone going to be 0

481

00:21:03,400  -->  00:21:06,066
so which implies that value is equal to 0

482

00:21:06,866  -->  00:21:08,666
your potential inside that uh

483

00:21:09,100  -->  00:21:11,233
a conductor is going to be 0

484

00:21:11,266  -->  00:21:14,800
so this implies that value is equal to 0

485

00:21:14,800  -->  00:21:18,366
so what happens that throughout

486

00:21:18,366  -->  00:21:20,100
throughout the conductor

487

00:21:20,266  -->  00:21:23,400
the potential is going to be the same

488

00:21:23,400  -->  00:21:25,366
so it that's why we

489

00:21:25,733  -->  00:21:29,700
we see that a conductor is an equal potential body

490

00:21:29,700  -->  00:21:33,200
because it's difference or it's differential

491

00:21:33,200  -->  00:21:35,733
electric potential is equal to zero

492

00:21:35,733  -->  00:21:36,900
there's no rate of change

493

00:21:36,900  -->  00:21:39,366
there's no change in the potential

494

00:21:39,533  -->  00:21:42,700
over the entire surface of that conductor

495

00:21:42,766  -->  00:21:44,400
so it is only because

496

00:21:45,600  -->  00:21:48,066
uh because of it's uh

497

00:21:48,066  -->  00:21:48,733
a property

498

00:21:48,733  -->  00:21:52,100
that there's no internal electric cream inside the

499

00:21:52,100  -->  00:21:53,800
electric inside the conductor

500

00:21:54,366  -->  00:21:56,333
and once we involve the gauze store

501

00:21:56,333  -->  00:21:59,000
we know that it is the close integral surface integral

502

00:21:59,000  -->  00:22:02,266
Audi dot DS where we is equal to the volume

503

00:22:02,566  -->  00:22:05,700
open volume to grab volume chart density

504

00:22:05,700  -->  00:22:07,100
now in this case if your

505

00:22:07,100  -->  00:22:10,933
this thing is equal to 0 and this thing is equal to 0

506

00:22:10,933  -->  00:22:13,966
this this means your left hand is equal to 0

507

00:22:13,966  -->  00:22:17,200
and it is only possible if your right hands

508

00:22:17,266  -->  00:22:19,400
inside parameter is equal to 0

509

00:22:19,400  -->  00:22:22,166
so for the so that thing that's why we say that roll

510

00:22:22,166  -->  00:22:24,200
these are also equal to zero

511

00:22:24,266  -->  00:22:26,533
so this is your takeaway from these two slides

512

00:22:26,533  -->  00:22:30,200
that inside an isolated perfect conductor

513

00:22:30,266  -->  00:22:31,700
your electric rate is zero

514

00:22:31,700  -->  00:22:37,066
hence your uh this uh VAB or LB is equal to 0

515

00:22:37,200  -->  00:22:40,133
and uh uh likewise your

516

00:22:40,133  -->  00:22:43,166
this uh volume chart density is equal to zero

517

00:22:43,333  -->  00:22:45,366
here we define that the AB is differential

518

00:22:45,366  -->  00:22:48,700
difference between two points a and B in t conduct

519

00:22:50,400  -->  00:22:51,733
now what's uh what happens

520

00:22:51,733  -->  00:22:54,666
uh once we apply the external field

521

00:22:54,733  -->  00:22:57,466
uh using this uh batteries right

522

00:22:57,466  -->  00:22:58,166
and this uh

523

00:22:58,166  -->  00:23:01,366
this potential extended potential or batteries

524

00:23:01,366  -->  00:23:06,200
you can see that so once we apply this voltage

525

00:23:06,200  -->  00:23:08,333
once we apply this voltage across the conductor

526

00:23:08,333  -->  00:23:09,566
let's see what happens so

527

00:23:09,566  -->  00:23:11,966
when a potential difference is applied

528

00:23:11,966  -->  00:23:13,600
at the ends of conductors

529

00:23:13,600  -->  00:23:16,333
so in that case we will have some

530

00:23:16,333  -->  00:23:19,766
we will have some electric field inside that conductor

531

00:23:19,766  -->  00:23:20,066
so

532

00:23:20,066  -->  00:23:23,000
electric field is not equal to zero for the conductor

533

00:23:23,000  -->  00:23:25,466
once the potential is being applied

534

00:23:25,466  -->  00:23:26,933
across the conductor

535

00:23:26,933  -->  00:23:30,100
so in this case the conductor is not isolated

536

00:23:30,300  -->  00:23:33,000
it is a wide it is wide to a source

537

00:23:33,966  -->  00:23:34,366
hence

538

00:23:34,366  -->  00:23:37,500
an electric field must exist inside the conductor

539

00:23:37,500  -->  00:23:39,566
to sustain the flow of electrons

540

00:23:40,066  -->  00:23:41,866
the direction of electric field

541

00:23:42,300  -->  00:23:43,333
the direction of electricity

542

00:23:43,333  -->  00:23:46,366
so we know that under the impact of electric feed

543

00:23:46,566  -->  00:23:48,133
uh the electro

544

00:23:48,133  -->  00:23:50,366
and the positive charges will move in one direction

545

00:23:50,366  -->  00:23:52,933
and negative charges will move in other direction

546

00:23:52,933  -->  00:23:55,966
so in this particular case it is your positive

547

00:23:55,966  -->  00:23:57,166
it is your negative

548

00:23:58,200  -->  00:24:00,200
so electrical direction is like this

549

00:24:00,200  -->  00:24:02,866
so your positive charges direction

550

00:24:02,933  -->  00:24:05,933
conventionally will be also in the direction of it

551

00:24:05,933  -->  00:24:09,466
inside electric field and your uh electrons

552

00:24:09,466  -->  00:24:12,100
it will it will move in the opposite direction

553

00:24:12,766  -->  00:24:15,100
so the direction of electric feed produced

554

00:24:15,100  -->  00:24:17,933
is the same as the direction of

555

00:24:17,933  -->  00:24:19,733
the flow of positive charges

556

00:24:19,733  -->  00:24:22,800
or the current so conventionally what we say that

557

00:24:22,800  -->  00:24:26,266
that it is our flow of positive charges

558

00:24:26,733  -->  00:24:28,600
the direction of flow of positive charges

559

00:24:28,600  -->  00:24:30,633
taken as the direction of your current

560

00:24:31,366  -->  00:24:34,266
and uh this direction is opposite to the direction of

561

00:24:34,266  -->  00:24:35,900
uh floor of electrons

562

00:24:35,900  -->  00:24:40,066
and the opposition to any opposition to the floor of uh

563

00:24:40,066  -->  00:24:41,366
this uh electrons

564

00:24:41,366  -->  00:24:46,000
or these politic charges is known as the resistance of

565

00:24:46,000  -->  00:24:47,266
uh uh the conductor

566

00:24:48,600  -->  00:24:50,000
to divide the resistance

567

00:24:50,000  -->  00:24:51,700
the magnitude of electric wheel

568

00:24:51,700  -->  00:24:52,566
we know that

569

00:24:52,566  -->  00:24:58,166
we have already defined that we equal to E dot DL right

570

00:24:59,733  -->  00:25:02,766
and then we define that if this is a complete land

571

00:25:02,766  -->  00:25:06,533
we can also needed that be equal to Ed like this thing

572

00:25:06,533  -->  00:25:08,966
right generalize in this thing

573

00:25:08,966  -->  00:25:10,900
we can also generalize it like this

574

00:25:11,166  -->  00:25:12,366
so this example

575

00:25:12,366  -->  00:25:15,766
your d is the complete land of your conductor

576

00:25:15,766  -->  00:25:18,700
and this is your externally applied voltage

577

00:25:19,766  -->  00:25:20,500
uh okay

578

00:25:20,500  -->  00:25:21,366
involve this equation

579

00:25:21,366  -->  00:25:23,833
so is equal to the ratio of from here

580

00:25:24,000  -->  00:25:27,266
your E is equal to be upon d to this L

581

00:25:27,400  -->  00:25:30,366
and assuming the conductor has a uniform cross section

582

00:25:30,366  -->  00:25:31,166
that is s

583

00:25:31,166  -->  00:25:34,866
so no involve the definition of this current density

584

00:25:34,866  -->  00:25:37,300
that is the ratio of your current surface area

585

00:25:37,933  -->  00:25:41,666
and also you know that J z go to Sigma e right

586

00:25:41,666  -->  00:25:43,466
so from here you can er

587

00:25:45,000  -->  00:25:46,166
equate equate these two things

588

00:25:46,166  -->  00:25:47,900
so J Z go to Sigma e right

589

00:25:48,366  -->  00:25:51,400
so from here you plug in this E

590

00:25:51,600  -->  00:25:53,733
E inside this right

591

00:25:53,733  -->  00:25:56,266
and then rearrange then rearrange the equation

592

00:25:56,266  -->  00:25:58,066
such that on the left hand side

593

00:25:58,066  -->  00:26:01,966
we have B ratio v upon I and on right side we will

594

00:26:01,966  -->  00:26:05,066
we will we will be left with L divide by Sigma s

595

00:26:05,700  -->  00:26:07,100
so now in while the ONSAR

596

00:26:07,100  -->  00:26:10,533
so we know that from ONS rise we we equal to I R

597

00:26:10,533  -->  00:26:12,600
so I is equal to V upon I

598

00:26:12,700  -->  00:26:15,900
and from here you can introduce that your resistant

599

00:26:16,166  -->  00:26:20,666
resistance your resistance is equal to uh

600

00:26:20,666  -->  00:26:23,300
it is directly proportional to the length of conductor

601

00:26:23,300  -->  00:26:26,566
and inversely proportional to the surface area of that

602

00:26:26,566  -->  00:26:29,066
conductor and this is our main assumptions as well

603

00:26:29,066  -->  00:26:31,433
that we are studying in our earlier classes as well

604

00:26:31,700  -->  00:26:33,200
and this construct of integration

605

00:26:33,200  -->  00:26:35,533
it is proportionality constant

606

00:26:35,533  -->  00:26:37,400
in this case is 1 upon Sigma

607

00:26:37,400  -->  00:26:40,400
and it can be defined as this row c

608

00:26:40,400  -->  00:26:43,866
that is your resistivity in this particular case

609

00:26:43,966  -->  00:26:47,466
so it is the reciprocal of your conductivity

610

00:26:48,333  -->  00:26:50,066
so the cross section of the conductor

611

00:26:50,066  -->  00:26:52,866
it is not uniform then we involve the integrations

612

00:26:52,866  -->  00:26:54,166
integrals right

613

00:26:54,466  -->  00:26:57,300
so for this we know that we equal to minus uh

614

00:26:57,300  -->  00:27:00,333
integral of e dot d l and then we know that this I

615

00:27:00,333  -->  00:27:03,966
I is equal to what was I I was equal to

616

00:27:04,500  -->  00:27:04,800
you know

617

00:27:04,800  -->  00:27:08,700
remember that it was equal to j dot this thing right

618

00:27:08,700  -->  00:27:10,500
if this is not a uniform

619

00:27:10,500  -->  00:27:12,700
then we can involve this in CHIGRE

620

00:27:14,800  -->  00:27:16,866
that we defined on the previous life

621

00:27:18,700  -->  00:27:20,733
so remember that uh your resistant

622

00:27:20,733  -->  00:27:21,900
it is directly proportional

623

00:27:21,900  -->  00:27:24,000
it increases with the length of your

624

00:27:24,000  -->  00:27:25,566
with uh uh conductor

625

00:27:25,566  -->  00:27:26,466
and it decreases

626

00:27:26,466  -->  00:27:29,266
as we increase the surface of your conductor

627

00:27:30,600  -->  00:27:34,600
uh no extra study what is part and what and what part

628

00:27:34,600  -->  00:27:35,733
part and part

629

00:27:35,733  -->  00:27:40,366
once your current is flowing through that uh

630

00:27:40,366  -->  00:27:42,733
conductor and what the uh

631

00:27:42,733  -->  00:27:45,966
floor for charges in inside that conductor

632

00:27:45,966  -->  00:27:47,600
so first of all it depart

633

00:27:47,600  -->  00:27:50,733
it is defined as the rid of

634

00:27:50,733  -->  00:27:53,366
change of energy that is in your

635

00:27:53,366  -->  00:27:55,400
in your jaws and uh

636

00:27:55,400  -->  00:27:58,533
are also it is defined at the four times the velocity

637

00:27:58,533  -->  00:28:01,866
so we we we're using this definition over here

638

00:28:01,933  -->  00:28:05,133
and we involve the dark product over here from uh

639

00:28:05,133  -->  00:28:07,500
kulinstar we know that Africa Q E

640

00:28:07,600  -->  00:28:09,466
and that we know that is your cue

641

00:28:09,466  -->  00:28:10,800
your cue is equal true

642

00:28:12,133  -->  00:28:14,233
Roby where's your cube

643

00:28:15,466  -->  00:28:19,066
that is your Roby in two

644

00:28:22,366  -->  00:28:23,666
yeah so yeah

645

00:28:23,666  -->  00:28:28,200
it is your volume in general or your volume

646

00:28:28,200  -->  00:28:30,700
volume chart density right so this thing

647

00:28:32,366  -->  00:28:34,000
like this thing you can enroll it

648

00:28:34,000  -->  00:28:37,700
right or not rearrange this equation in this manner

649

00:28:37,733  -->  00:28:40,600
and then we what we can define now

650

00:28:40,600  -->  00:28:45,366
so here here you remember this definition of your G

651

00:28:45,566  -->  00:28:47,700
so this is your G in this case

652

00:28:48,566  -->  00:28:50,600
the current density that we define

653

00:28:50,800  -->  00:28:53,066
so it is the product of your volume

654

00:28:53,066  -->  00:28:55,166
your volume identity times b

655

00:28:55,600  -->  00:28:57,333
either it is drift losty

656

00:28:57,333  -->  00:29:00,400
or it is the motion of electron losty

657

00:29:00,400  -->  00:29:02,800
for the case of correction

658

00:29:02,800  -->  00:29:04,733
so here we are talking about the drift losty

659

00:29:04,733  -->  00:29:07,600
because we are talking about the conductors here

660

00:29:08,400  -->  00:29:10,633
okay now this is known as the jewels laws right

661

00:29:10,800  -->  00:29:14,700
so jewels law jewels law estate

662

00:29:14,700  -->  00:29:15,466
uh uh

663

00:29:15,466  -->  00:29:16,800
so and we can uh

664

00:29:16,800  -->  00:29:19,700
what we can probably simplify this is not your TV

665

00:29:19,700  -->  00:29:21,966
TV is equal to your differential

666

00:29:21,966  -->  00:29:25,100
volume is equal to your differential surface and

667

00:29:26,333  -->  00:29:27,900
differential current right

668

00:29:29,166  -->  00:29:30,766
not involve these things

669

00:29:30,866  -->  00:29:33,166
separate these two these two things

670

00:29:33,166  -->  00:29:36,933
separate these two things that take the length

671

00:29:36,933  -->  00:29:38,133
differential long days

672

00:29:38,133  -->  00:29:40,533
take the volume differential long days

673

00:29:40,533  -->  00:29:42,533
and then involve the further definition

674

00:29:42,533  -->  00:29:43,966
that we have already died

675

00:29:44,133  -->  00:29:47,266
so this V is equal to the integral of e dot DL

676

00:29:47,266  -->  00:29:49,133
and your uh uh

677

00:29:49,133  -->  00:29:52,733
I is it nest is the surface integral of your uh

678

00:29:52,733  -->  00:29:55,333
your density right so here you can present

679

00:29:55,333  -->  00:29:57,300
while the top products over here right

680

00:29:57,300  -->  00:29:59,166
like this thing the C

681

00:30:01,266  -->  00:30:03,100
okay once we once we simplify

682

00:30:03,100  -->  00:30:05,733
so this is the general bar equation

683

00:30:05,733  -->  00:30:08,466
that we utilize in our physics

684

00:30:08,466  -->  00:30:11,200
and it will further involve the arms law

685

00:30:11,200  -->  00:30:14,133
then it can be inerated in terms of holy

686

00:30:14,133  -->  00:30:17,366
and solely the current flowing through that conductor

687

00:30:17,366  -->  00:30:20,433
and it is a studio resistance of that conductor

688

00:30:20,600  -->  00:30:24,566
so it simply involve further that your vis equal to IR

689

00:30:24,766  -->  00:30:26,366
that is your vis equal to IR

690

00:30:26,366  -->  00:30:29,266
then it is your second definition of your FA

691

00:30:29,266  -->  00:30:32,266
that is your vis is equal to I squared out

692

00:30:32,400  -->  00:30:33,566
so these two equations

693

00:30:33,566  -->  00:30:36,900
they are known as the Jules law and once said

694

00:30:36,900  -->  00:30:38,566
we also define another technology

695

00:30:38,566  -->  00:30:39,933
that is your PA density so

696

00:30:39,933  -->  00:30:41,666
it is the rate of change of PA

697

00:30:42,333  -->  00:30:44,266
with respect to your volume

698

00:30:44,266  -->  00:30:47,900
so differential so it is your differential

699

00:30:49,600  -->  00:30:53,000
change in the PA with respect to differential volume

700

00:30:53,866  -->  00:30:55,133
so if we see here

701

00:30:55,133  -->  00:30:58,366
so it is basically your intigland intigland

702

00:30:58,900  -->  00:31:02,600
intigland inside this equation like this one right

703

00:31:03,966  -->  00:31:07,066
so it is your e dot g

704

00:31:07,066  -->  00:31:09,633
and then we involve g is equal to Sigma e

705

00:31:10,200  -->  00:31:13,066
right then e dot e equal

706

00:31:13,066  -->  00:31:13,700
we know that

707

00:31:13,700  -->  00:31:16,400
it is the magnitude scale of that vector quantity

708

00:31:16,400  -->  00:31:20,066
so this is your this is your PR dense t

709

00:31:20,066  -->  00:31:23,166
which is your wrt per cubic meter

710

00:31:25,800  -->  00:31:28,800
let's solve these examples of your book

711

00:31:29,100  -->  00:31:31,566
so that you can further understand

712

00:31:31,566  -->  00:31:34,666
these concepts of current density

713

00:31:34,766  -->  00:31:35,733
and how to find out

714

00:31:35,733  -->  00:31:38,200
the current passing to the surface areas

715

00:31:38,200  -->  00:31:39,600
so first first of all

716

00:31:39,600  -->  00:31:41,866
let's consider this example 5.1

717

00:31:41,866  -->  00:31:45,266
so in this case you are given with current er density

718

00:31:45,333  -->  00:31:46,333
the volume current density

719

00:31:46,333  -->  00:31:48,366
you can see here the surface condensity

720

00:31:48,366  -->  00:31:49,666
so it is a volume current density

721

00:31:49,666  -->  00:31:53,100
because it is m pairs per cubic uh meter

722

00:31:53,766  -->  00:31:55,100
okay and uh

723

00:31:55,100  -->  00:31:57,333
we need to calculate the current passing through

724

00:31:57,333  -->  00:32:00,133
a hemispherical shell it is a hemispherical

725

00:32:00,133  -->  00:32:02,700
so that's why is theatre range it is from 0

726

00:32:02,700  -->  00:32:05,766
2 5 by 2 for a complete vertical shell it is from 0

727

00:32:05,766  -->  00:32:06,166
2 pi

728

00:32:06,166  -->  00:32:10,000
that is the difference and for 5 it is it is the same

729

00:32:10,000  -->  00:32:11,600
that is 0 0

730

00:32:11,600  -->  00:32:16,000
2 2 pi ladies is given in these two cases only

731

00:32:16,000  -->  00:32:17,366
the thing that we need to do is

732

00:32:17,366  -->  00:32:20,600
we need to take the integration of this

733

00:32:21,733  -->  00:32:26,800
this volume chart density with respect to this volume

734

00:32:26,800  -->  00:32:32,200
current density with respect to this circus that think

735

00:32:32,200  -->  00:32:34,933
right surface surface yeah

736

00:32:34,933  -->  00:32:37,100
surface differential surface element

737

00:32:37,466  -->  00:32:40,166
okay we know that train this vertical coordinate system

738

00:32:40,166  -->  00:32:40,866
your DS

739

00:32:40,866  -->  00:32:45,500
it is equal to rscare assigned Peter Dyd Peter er

740

00:32:45,600  -->  00:32:48,900
and here since it is involved in body dot product

741

00:32:48,900  -->  00:32:52,200
so only this component will see after this dot product

742

00:32:52,400  -->  00:32:53,366
right this thing

743

00:32:53,666  -->  00:32:55,000
now to simplify this thing

744

00:32:55,000  -->  00:32:57,866
your R is going since both are integrations

745

00:32:57,866  -->  00:33:00,300
they are both with this back to defiant heater

746

00:33:00,300  -->  00:33:03,666
so R is going to come out as a constant

747

00:33:03,700  -->  00:33:06,600
and for the first case your R is point two

748

00:33:06,600  -->  00:33:08,866
for the second case your R is point one

749

00:33:09,866  -->  00:33:12,700
no due to the integration in this example

750

00:33:12,700  -->  00:33:13,800
you can see that

751

00:33:14,000  -->  00:33:17,233
you can involve this product rule of the integration

752

00:33:17,500  -->  00:33:19,000
or the substitution rule

753

00:33:19,000  -->  00:33:23,100
that here we have the differentiation of sign theater

754

00:33:23,100  -->  00:33:24,566
along with this so

755

00:33:24,566  -->  00:33:28,100
it's integration is Science Square data divided by two

756

00:33:28,100  -->  00:33:30,100
right or you can see that

757

00:33:30,100  -->  00:33:32,700
you can see that you involve this barrel

758

00:33:32,700  -->  00:33:34,300
using this substitution

759

00:33:34,300  -->  00:33:36,933
that you have this usable to sign theatre

760

00:33:36,933  -->  00:33:39,300
and replace this d usable to cost theatre

761

00:33:39,300  -->  00:33:40,100
d theatre

762

00:33:40,333  -->  00:33:43,266
and then you just integrate it and put in these values

763

00:33:43,266  -->  00:33:44,866
and constant values of the radius

764

00:33:44,866  -->  00:33:49,933
so this is your crime and once it is a complete square

765

00:33:49,933  -->  00:33:53,366
then you have to simply change the values

766

00:33:53,366  -->  00:33:55,166
limits of this data from t 2 2

767

00:33:55,166  -->  00:33:57,266
5 and alternatively

768

00:33:57,266  -->  00:34:00,066
the other way is from your divergence

769

00:34:00,066  -->  00:34:01,466
theodom that is your

770

00:34:01,466  -->  00:34:03,466
you know that it is your divergence theodom

771

00:34:06,766  -->  00:34:11,000
right so a closing trigger log for s g dot d s

772

00:34:11,000  -->  00:34:15,800
no y closing trigger because it is a complete volume

773

00:34:15,800  -->  00:34:18,600
the complete sphere in this case the Smetri

774

00:34:18,600  -->  00:34:20,800
Smetri in this case is very good

775

00:34:21,733  -->  00:34:22,800
so for this case

776

00:34:22,800  -->  00:34:26,200
uh you can use the divergence uh theorem

777

00:34:26,200  -->  00:34:26,766
so

778

00:34:26,766  -->  00:34:30,266
and that is the part of the open volume table of this

779

00:34:30,266  -->  00:34:31,666
at the dot g

780

00:34:31,866  -->  00:34:34,900
and if we if you take the divergence of this thing

781

00:34:34,900  -->  00:34:37,700
divergence of this G with respect to this

782

00:34:38,000  -->  00:34:40,933
and that low pressure in this vertical gardener system

783

00:34:40,933  -->  00:34:43,000
you will find that that dot g is equal to zero

784

00:34:43,000  -->  00:34:45,166
so again the current is going to be zero

785

00:34:45,166  -->  00:34:48,733
so this is your alternative way for the closed volumes

786

00:34:48,733  -->  00:34:50,433
remember for the closed volumes

787

00:34:52,400  -->  00:34:54,266
let's consider an another example

788

00:34:54,266  -->  00:34:54,500
so

789

00:34:54,500  -->  00:34:57,933
here we are having a y with the diameter 1 millimeter

790

00:34:57,933  -->  00:35:00,766
conducted at the given m s bars

791

00:35:00,766  -->  00:35:04,400
and each 7 piece number of electrons per cubic meter

792

00:35:04,400  -->  00:35:05,933
flowing and electric

793

00:35:05,933  -->  00:35:08,666
external electric grid is 10 milliwatt per meter

794

00:35:08,933  -->  00:35:09,066
now

795

00:35:09,066  -->  00:35:11,933
we need to find all the chart as your free electrons

796

00:35:11,933  -->  00:35:14,200
first of all the volume chart density

797

00:35:14,200  -->  00:35:16,700
so that's the product of your number of electrons

798

00:35:16,700  -->  00:35:18,133
times the uh

799

00:35:18,133  -->  00:35:19,733
charge of your single electrons

800

00:35:19,733  -->  00:35:21,600
so this is your volume chart density

801

00:35:23,100  -->  00:35:26,733
okay and uh what else because here

802

00:35:26,733  -->  00:35:27,000
you know

803

00:35:27,000  -->  00:35:30,533
that it is your number of electrons per cubic volume

804

00:35:30,533  -->  00:35:32,133
so this is per cubic volumes

805

00:35:32,133  -->  00:35:35,066
that say your manager has seen this

806

00:35:35,066  -->  00:35:37,433
uh mission at all per cubic volume

807

00:35:37,933  -->  00:35:39,933
and then as you need to find out the current density

808

00:35:39,933  -->  00:35:43,866
it is a Sigma times e lactropine Sigma

809

00:35:43,866  -->  00:35:45,933
what is Sigma this is your conductivity

810

00:35:45,933  -->  00:35:50,000
510 days for 7 and e 10 millimeterwatts like this

811

00:35:50,333  -->  00:35:53,766
then current it is the product of G dot s and what is s

812

00:35:54,333  -->  00:35:57,066
from here we have the diameter and radius

813

00:35:57,066  -->  00:35:59,100
we know that it is the half of the diameter

814

00:35:59,100  -->  00:36:03,766
so for the surface it is by our scale for this uh

815

00:36:04,066  -->  00:36:06,933
for this uh diameter for this circular surface

816

00:36:06,933  -->  00:36:09,733
right by your scale so you can solve this thing

817

00:36:09,733  -->  00:36:13,466
and then uh we know that J is equal to rule v

818

00:36:13,800  -->  00:36:17,200
uh Zhu and uh we need to find out the drift lost E

819

00:36:17,200  -->  00:36:18,866
right and drift lost E is

820

00:36:18,866  -->  00:36:22,533
is equal to J divided by 4 v and Jay

821

00:36:22,533  -->  00:36:25,500
we have Drive Ruby we have drive so simply solve this

822

00:36:27,133  -->  00:36:27,933
uh no uh

823

00:36:27,933  -->  00:36:29,400
we have to find out uh

824

00:36:29,400  -->  00:36:34,200
the resistance for this uh for this uh bar

825

00:36:34,200  -->  00:36:36,533
which is having the lent of 4 metre

826

00:36:36,533  -->  00:36:38,366
and having the cross sectional area

827

00:36:38,933  -->  00:36:42,566
cross sectional area of 3 by 3 right

828

00:36:42,566  -->  00:36:44,900
but in inside that there's a pole

829

00:36:44,900  -->  00:36:45,733
there's a hole

830

00:36:45,733  -->  00:36:48,566
hole that is running along the complete lent of

831

00:36:48,800  -->  00:36:51,000
learning along the complete lent of like this

832

00:36:51,000  -->  00:36:52,866
you can assume which is the complete length

833

00:36:53,200  -->  00:36:56,200
complete dental this conductor like so

834

00:36:56,200  -->  00:36:58,200
if you can assume it is 4 m

835

00:36:58,466  -->  00:37:01,000
so how to find out its surface area

836

00:37:01,266  -->  00:37:02,166
first of all

837

00:37:02,766  -->  00:37:04,400
we have to subtract this

838

00:37:05,400  -->  00:37:09,166
all surface area from the surface area of this square

839

00:37:09,166  -->  00:37:12,333
so that is your uh uh 9 9

840

00:37:12,333  -->  00:37:13,000
the 3 square

841

00:37:13,000  -->  00:37:16,800
minus by your scale to the radius is half of your dial

842

00:37:17,000  -->  00:37:17,600
so what is diet

843

00:37:17,600  -->  00:37:21,200
diet is given as a 1 cm take care of these visioners

844

00:37:21,200  -->  00:37:23,933
the radius is given in the centimeters

845

00:37:23,933  -->  00:37:25,866
diameters and all the dimensions

846

00:37:25,866  -->  00:37:28,000
they are given in this centimeter here in this case

847

00:37:28,400  -->  00:37:32,066
so your surface area the surface area of the effective

848

00:37:32,133  -->  00:37:35,233
conductive part of this ledge

849

00:37:36,733  -->  00:37:42,366
lead material made bar it is the 9 minus five by 4

850

00:37:42,600  -->  00:37:44,700
and then from here you can find out the resistance

851

00:37:44,700  -->  00:37:46,466
that is the L dividers of my ass

852

00:37:46,466  -->  00:37:49,600
no LD is before and this is your your

853

00:37:50,000  -->  00:37:52,600
your remaining surface of your

854

00:37:52,600  -->  00:37:56,066
that part and then simplify this thing

855

00:37:56,766  -->  00:37:59,066
so in today's lecture we understood what are different

856

00:37:59,066  -->  00:38:01,100
what are the properties of materials

857

00:38:01,100  -->  00:38:03,533
and how to classify the materials

858

00:38:03,533  -->  00:38:05,066
based upon the conductivity

859

00:38:05,266  -->  00:38:07,966
and what ranges classify the conductors

860

00:38:08,066  -->  00:38:12,700
dialectrics and your semiconductors and uh

861

00:38:12,866  -->  00:38:15,066
and how they impact and uh

862

00:38:15,066  -->  00:38:17,566
how they impact the electric grid of the conductors

863

00:38:17,566  -->  00:38:20,866
and this we will study in upcoming uh lectures as well

864

00:38:21,900  -->  00:38:22,333
previously

865

00:38:22,333  -->  00:38:24,866
we started electrically inside the free space

866

00:38:25,066  -->  00:38:25,933
then we understood

867

00:38:25,933  -->  00:38:27,866
what is the difference between contraction

868

00:38:27,866  -->  00:38:29,166
and conduction currents

869

00:38:29,166  -->  00:38:31,433
and we derived it questions as well

870

00:38:31,600  -->  00:38:33,366
followed by some examples

871

00:38:34,466  -->  00:38:36,666
in the next class we are going to study the

872

00:38:37,600  -->  00:38:40,300
what is the polarization in the dialectrics

873

00:38:40,300  -->  00:38:42,800
under the impact of external electric field

874

00:38:42,800  -->  00:38:44,733
we will understand what is the polarization

875

00:38:44,733  -->  00:38:46,933
and determine the polarization

876

00:38:46,933  -->  00:38:49,566
and then we will determine the dialectic constant

877

00:38:49,566  -->  00:38:53,466
and the strength of the these dialectic materials

878

00:38:56,966  -->  00:38:58,200
here I thank you all

879

00:38:58,200  -->  00:39:00,166
if you have any questions uh

880

00:39:00,166  -->  00:39:01,566
they will be entertained uh

881

00:39:01,566  -->  00:39:03,900
through your emails or online

882

00:39:03,900  -->  00:39:05,000
synchronous sessions

883

00:39:05,000  -->  00:39:07,566
that we have arranged at the department