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this is election No. 16 of a V232

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electromagnetic field theory

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today we study polarization in dielectrics

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and dielectric core strength

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and strength of being dielectrics

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it should cover your

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section 5.5 and 5.6 of your textbook

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the learning objectives of today's electric

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would be to understand and determine the polarization

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dialectrics and then determine the dialect constant

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and the strength of the dialectry

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under the influence of external electric field

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now first of all

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uh again recap what is conductor and dialectry

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the main difference between our conductor and

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dialectry is the availability of free electrons

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in the atomic outermost shells to conduct current

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so for the conductor uh

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there are more number of free electrons

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whereas in the dialectors

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there least number of electrons

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in dialectry materials

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charges are not able to move about freely

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right and they are bound by finite forces

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and displacement is expected only once

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and external freely is applied right

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so remember that in this particular case the electrons

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they are not freely available

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they are bounded with some forces

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and the only way to displace them is to apply

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external force

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so atoms or molecules are electrically neutral

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this we know that uh that uh uh the electrons

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uh the electrons and uh the positive uh postrons

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uh they will eliminate the effect of each other right

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protons and

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since the positive and negative

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charges have an equal amount

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so they will cancel out

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so because the net charge of electrons and the protons

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that is equal in magniture

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so they will eliminate each other

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now if we see

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we consider the things that macroscopic effect then

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so natural

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macroscopic effect of electric field on a dialectory

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considered an atom of a dialectric

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as consisting of negative charges

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that is your electron cloud

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and for positive charges it is herbs and nucleus

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and similarly if we consider for the molecules

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right at the bigger

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more bigger level a similar picture can be adopted

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for a dialectric molecule

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the nuclei in the molecules

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can be treated as a positive point charges

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whereas the electronic structure has a single cloud of

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negative chart

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now let's discuss what is polarization in dialectrics

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when an external feel e is applies to what happens

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the positive charges so this is the state

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once there's no external electric feel applied

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and this is the case

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once external feel is being applied

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support posture

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charges are displaced from its ecliprian position

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in the direction of external electric field right

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the positive charges will move in the same direction

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that is the direction of your electric field

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and negative charges

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they will move in the opposite direction

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this will discuss in our previous lecture as well

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so

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the force being exerted by the external electric field

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it is for the posture charges

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it is Q e right

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and similarly for the negative charges

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it is in the opposite direction

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so it is again the Q e

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and since Q is in magnitude it is same in both

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in both cases so a Dipo

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so what happens

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that a Dipo reserves from the displacement of charges

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and the dialectic is set to be polarized

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so under the impact of external electrified

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the uh the dialectrics is set to be polarized

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and how does this dipole uh

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dipole is the coming into K or coming into build up

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that your positive charges are going over here

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your negative charges are piling over here

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and it will see in this figure in polar state

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the electron cloud is distorted by the external E field

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the distorted charge distribution is equaled by

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principal of superposition

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so you can consider like this way

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that it is your original

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it is your original charge distribution inside the uh

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inside the uh this uh

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whatever molecule or electron or dielectric

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which is having a distribution of electron

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atoms and molecules and plus

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a dipole is building up areas where deposit charges

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going on the right hand side

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in the direction of your external e feel

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and possible charge charges building up on the

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it's left hand side here so

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so you can see that in the poor eyes straight

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that the distorted charge distribution is equivalent

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by the principle of superposition

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to the original charge distribution

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that is your

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without the influence of external electrical

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plus a dipal movement which has created

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due to the deformation of molecules

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under the impact of your external electrical

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so that

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they are forming upper upon a typal moment over here

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now if we see this thing

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in terms of mathematical formulation

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so a typal typal moment is created

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so in this case this the distance

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the smaller distance

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between the negative and positive charge

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accumulation of this typole

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and if there are a number of typoles are building up

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then we know that

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it is simply a superposition of each of the typoles

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that we cater them in the form of mission

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and as a major of intensity of polarization

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now let's define a term polarization

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so the polarization it is defined as the typo moment

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typo moment per unit volume

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so the total typo

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so the total diaper moment per unit volume right

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so it is in the coolums per meter scale right

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so as you can see here that it is coolum in 2 meter

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and it is meter cube right

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so after translation it is coolum per meter scale

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there are generally two groups of uh dialectrics

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the first one is the non polar

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and the second one is the polar

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so non polar dialectric molecules don't possess diples

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they don't possess diples

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until we apply an external electric fee

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so major effect of extra electric field on a dialectry

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is the creation of the type of moments

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that align themselves in the direction of external

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electrically

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that we discussed in the previous site as well

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so the examples of non prototypes of dielectrics are

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hydrogen oxygen

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nitrogen and rare gases that is your neon

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your krypron your argan your xenon yeah

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you can study on the internet as well uh

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and then what is polar polydylectrics

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so in the polydylectrics

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molecules have built in permanent dipoles

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so they already have the typos between

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in them by default

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and that they are randomly orientated

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so in this case you can see

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they are randomly oriented in different direction

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and once we apply the external electric fee

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the typo movements are get

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get themselves aligned

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in the direction of external electric fee

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so polarization of porno molecules

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so it is in the in the first direction

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it is in the first figure a

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it's a permanent iPod

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without an external electric field

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and it is getting its set line in the directional

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external electric field

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once we apply the external electric field

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so the examples are your water

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your sulfur dioxide and hydrochloricasia

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so when uh when polarization occurs

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two charge identities are forming up

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so what are those two first one is if on its surface

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and the second one is inside its warning surface

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and warning so an equivalent surface chart density

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raw PS is formed over the surface of the dialectry

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and where in this particular

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in the particular case we relate this thing at the top

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product with the normal office surface

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and it is

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is polarization so that we discuss what it is

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it is the sum of the diable moment per unit volume

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okay and what is forming up inside its volume

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that is related with rope BB

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and it is the divergence of

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it is related as the minus divergence of its orization

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uh uh

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in this uh

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case there is a differentiation between the uh

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this circus

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and volume chart densities that we discussed earlier

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so they were free they were free chart densities

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we are whereas in this case

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we are having bound

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are surface and volume chart densities

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because they have been created

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under the influence of external electrical

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because the uh dialectric has been polarised

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in this case

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no bond

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charges

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are those that are not free to move within the dialect

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material and they are caused by the displacement

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that occurs on the molecules

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scale during polarization

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so bonding is always related under

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due to the external electric field

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and free charges are those that are capable of moving

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or microscopic distances for example

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the electrons in a conductor

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and the other stuff that we control

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once we apply the external voltages

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or the external fields

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so this is the difference between these two things

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if the entire dialectric were electrically neutral yes

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we know uh

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and prior to the application of electric field

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and if we are we have not added an additional field

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additional charge Ruby inside that dialectic

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we haven't added an additional charge inside it

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then the dialect will remain electrical neutral

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uh even if we apply the uh external electric fuel so uh

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if we if

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uh electric fuel

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if a dialectric is electrically neutral

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prior to the electric wheel

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and if we haven't added an additional charge into it

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then it will stay electrical neutral

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even if we apply the external field

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that is we

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it is coming into the polarization state

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the tutorial charge of the dialectic remains zero

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because of its neutrality

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and uh

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here we can see that uh

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there again due to this thing

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the surface charges and the warning charges

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they will be equal in magnitude

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but they will be opposite in uh

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in the quality

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so that they can cancel out each other's impact

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uh if we consider for the surface charges

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uh for the surface charges again

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it is uh

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for under the bound condition

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the total bound surface charges

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it is the uh

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surface integral of your bounded uh

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uh surface

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uh identity

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and uh

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we know we

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we we know by the definition it is p dot e n

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since it is a surface differentiality right

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you can write in the dark notation as well in this case

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00:11:43,733  -->  00:11:45,566
and in the second case uh

263

00:11:45,566  -->  00:11:46,500
your uh volume

264

00:11:46,500  -->  00:11:49,133
bounded volume it is uh charges

265

00:11:49,133  -->  00:11:50,000
they are uh

266

00:11:50,000  -->  00:11:51,300
equal to equal in magnitude

267

00:11:51,300  -->  00:11:53,566
but in the opposite direction to the

268

00:11:53,566  -->  00:11:55,500
that your surface chargers

269

00:11:55,533  -->  00:11:56,666
now in this case uh

270

00:11:56,666  -->  00:11:58,666
first of all you find this thing again

271

00:11:58,666  -->  00:12:00,966
by taking the volume trigger of this uh

272

00:12:00,966  -->  00:12:02,333
uh bounded volume

273

00:12:02,333  -->  00:12:05,600
uh chargers t and from the equation

274

00:12:05,600  -->  00:12:08,633
you know that it is minus dimensions of polarization

275

00:12:09,666  -->  00:12:12,066
put this thing back into this equation

276

00:12:12,066  -->  00:12:15,700
and if you see there that these two things

277

00:12:15,700  -->  00:12:19,700
these two things are also equal to each other

278

00:12:19,700  -->  00:12:23,133
due to this divergence theorem

279

00:12:23,133  -->  00:12:25,233
if you remember this thing right

280

00:12:25,266  -->  00:12:26,233
divergence theorem

281

00:12:26,333  -->  00:12:29,066
so they will also cancel out the industry as well

282

00:12:29,066  -->  00:12:31,066
and they will also cancel out industry as well

283

00:12:31,066  -->  00:12:34,300
that the next charge for this dialectric

284

00:12:34,300  -->  00:12:36,566
under the influence of external electrical

285

00:12:36,766  -->  00:12:39,366
will still equal to zero

286

00:12:40,066  -->  00:12:42,733
so that's why they will cancel out each other and that

287

00:12:42,733  -->  00:12:43,566
and that and the

288

00:12:43,566  -->  00:12:44,966
even under the polarization

289

00:12:44,966  -->  00:12:45,866
this will be

290

00:12:46,533  -->  00:12:50,166
this dialect will stay electrically neutral

291

00:12:51,800  -->  00:12:52,766
or if the

292

00:12:52,800  -->  00:12:56,933
if the dialectric region contains a free charge

293

00:12:56,933  -->  00:13:00,533
with a volume density of raw v right

294

00:13:00,533  -->  00:13:03,200
so the total volume charge density is the

295

00:13:03,200  -->  00:13:04,600
so now in this case

296

00:13:04,600  -->  00:13:07,966
there's an additional free charge density inside the

297

00:13:08,100  -->  00:13:10,200
inside the dialectly that is your Ruby

298

00:13:10,200  -->  00:13:12,900
which is your conventional chartency

299

00:13:13,000  -->  00:13:15,500
and no this is your chartency

300

00:13:15,500  -->  00:13:17,466
under the entrance of polarization

301

00:13:17,466  -->  00:13:19,200
so the overall chartency

302

00:13:19,200  -->  00:13:21,200
the overall total while in charge ency will be this

303

00:13:21,200  -->  00:13:22,366
some of these two

304

00:13:23,166  -->  00:13:27,133
now if we apply the Maxwell's first equation

305

00:13:27,133  -->  00:13:29,733
that is the divergence of your electric

306

00:13:29,733  -->  00:13:31,766
first density is equal to your

307

00:13:31,900  -->  00:13:33,766
this volume chart density

308

00:13:34,000  -->  00:13:35,266
uh then in this case you

309

00:13:35,266  -->  00:13:37,966
you know that d is equal to Abslineaut E

310

00:13:38,100  -->  00:13:39,766
and put that in uh

311

00:13:39,766  -->  00:13:42,533
Absline will come over here and uh

312

00:13:42,533  -->  00:13:43,400
put this uh

313

00:13:43,400  -->  00:13:45,766
route is equal to this mission of these tools

314

00:13:45,900  -->  00:13:48,700
volume chart and stays and then from here you can uh

315

00:13:48,700  -->  00:13:50,066
play around with equations

316

00:13:50,066  -->  00:13:51,000
you can uh

317

00:13:51,666  -->  00:13:52,066
yeah

318

00:13:52,066  -->  00:13:58,866
you can put this raw PV is equal to minus that dot b

319

00:13:59,966  -->  00:14:02,600
and then you rearrange this equation from here

320

00:14:02,600  -->  00:14:06,000
you take out this Ruby and then uh

321

00:14:06,000  -->  00:14:10,233
you can see that uh in this case is your density

322

00:14:10,533  -->  00:14:15,566
if you uh you have this analogy of this uh

323

00:14:16,266  -->  00:14:17,300
this like

324

00:14:17,300  -->  00:14:19,800
like this was your max or specification right

325

00:14:19,866  -->  00:14:22,700
if you have the analogy of these two things

326

00:14:22,966  -->  00:14:24,866
and you take out this rule in this case

327

00:14:24,866  -->  00:14:27,666
so in this case your d will be equal to this

328

00:14:27,666  -->  00:14:31,166
some of this astronaut E+ B

329

00:14:31,166  -->  00:14:32,400
so this means your

330

00:14:32,766  -->  00:14:35,100
your electric feel is going to increase

331

00:14:35,100  -->  00:14:36,833
inside the dialectric

332

00:14:37,066  -->  00:14:39,500
right inside the polarized dialectric

333

00:14:39,766  -->  00:14:43,866
so let's related to in terms of your definitions

334

00:14:43,866  -->  00:14:44,500
that

335

00:14:44,500  -->  00:14:49,200
application of external electric feel causes deflux

336

00:14:49,200  -->  00:14:52,066
density to be increased

337

00:14:52,800  -->  00:14:55,866
as it was uh without diploradation

338

00:14:55,866  -->  00:14:58,900
so without diploradation it was this one right

339

00:14:59,733  -->  00:15:00,100
so

340

00:15:00,100  -->  00:15:02,966
once it is coming under the influence of polarization

341

00:15:02,966  -->  00:15:05,866
under the influence of an external electric feel

342

00:15:05,900  -->  00:15:07,066
so what is going to happen

343

00:15:07,066  -->  00:15:10,633
the neck effect of dialectry on the electric feel

344

00:15:11,166  -->  00:15:17,100
is to increase d inside it by an amount of p

345

00:15:17,166  -->  00:15:19,500
and that p we have already defined what is that p

346

00:15:19,566  -->  00:15:21,533
so for the dialectry so

347

00:15:21,533  -->  00:15:25,166
the application of electric V to dialecting materials

348

00:15:25,166  -->  00:15:28,500
causes that is the under the polarization

349

00:15:28,733  -->  00:15:31,066
the electric field inside the dialect

350

00:15:31,066  -->  00:15:33,100
it is going to increase right

351

00:15:33,533  -->  00:15:34,666
uh causes the flux

352

00:15:34,666  -->  00:15:36,366
energy to be greater than it would be

353

00:15:36,366  -->  00:15:38,633
in the free space right

354

00:15:39,766  -->  00:15:42,166
once there will be no external electrical

355

00:15:42,166  -->  00:15:43,600
so remember that thing

356

00:15:43,600  -->  00:15:45,633
under the impact of external electrical

357

00:15:46,000  -->  00:15:47,766
the uh

358

00:15:47,766  -->  00:15:49,666
the neck electric field in uh

359

00:15:49,666  -->  00:15:52,500
inside the dialectic is going to the

360

00:15:52,500  -->  00:15:56,166
going to be increased by amount of P

361

00:15:57,533  -->  00:16:00,300
so polarization electrifying another term

362

00:16:00,300  -->  00:16:01,100
polarization

363

00:16:01,100  -->  00:16:03,833
is proportional to the applied electric field

364

00:16:04,066  -->  00:16:05,200
that is like this thing

365

00:16:05,200  -->  00:16:08,533
and these two are the constant of uh uh

366

00:16:08,533  -->  00:16:10,733
proportionalities and here this

367

00:16:10,733  -->  00:16:12,666
uh uh this

368

00:16:12,666  -->  00:16:13,466
uh

369

00:16:14,133  -->  00:16:15,466
Kai Kai you can say it

370

00:16:15,466  -->  00:16:17,866
Kai or shy will say it

371

00:16:17,866  -->  00:16:19,666
is genoted as

372

00:16:19,966  -->  00:16:22,800
the electric susceptibility of the material

373

00:16:23,266  -->  00:16:24,800
and susceptibility of material

374

00:16:24,800  -->  00:16:28,666
describes how quickly it responses

375

00:16:28,666  -->  00:16:31,600
or how immediately or how um

376

00:16:31,600  -->  00:16:35,700
effectively it responses to an external electric Bill

377

00:16:35,700  -->  00:16:39,266
and it is contributing towards its polarization shape

378

00:16:39,333  -->  00:16:43,400
so the higher this susceptibility often material

379

00:16:43,400  -->  00:16:45,400
the high will be its forization

380

00:16:45,400  -->  00:16:49,100
and high will be its internal increase

381

00:16:49,100  -->  00:16:50,300
in the dialectric

382

00:16:50,900  -->  00:16:54,800
in this electric grid density

383

00:16:57,466  -->  00:16:58,600
no betting on uh

384

00:16:58,600  -->  00:17:00,700
previous slide uh televisions

385

00:17:00,700  -->  00:17:03,866
uh we were to find that the uh overall

386

00:17:03,866  -->  00:17:04,866
uh dialectric

387

00:17:04,866  -->  00:17:05,666
uh

388

00:17:06,000  -->  00:17:07,666
this electric frequency

389

00:17:07,666  -->  00:17:12,233
is going to increase by the amount of polarization

390

00:17:12,566  -->  00:17:15,200
and if we involve the definition of this polarization

391

00:17:15,200  -->  00:17:17,366
we can rearrange this equation

392

00:17:17,366  -->  00:17:21,366
and then we can define further things that here

393

00:17:21,366  -->  00:17:24,433
right here this 1+ Chi

394

00:17:24,900  -->  00:17:28,933
1+ K is equal to your relative permittivity right

395

00:17:28,933  -->  00:17:30,266
relative parametivity

396

00:17:30,266  -->  00:17:32,300
remember it is relative permittivity

397

00:17:32,300  -->  00:17:36,500
and it is also defined as the ratio of your uh

398

00:17:36,666  -->  00:17:39,133
permittivity of dialect with uh

399

00:17:39,133  -->  00:17:42,500
with respect to the parametivity of uh free space

400

00:17:42,500  -->  00:17:46,933
that is your tenders from minus uh 9 / 36 pi r

401

00:17:46,933  -->  00:17:50,333
8.852 into tenders 12 minus twelve feathers

402

00:17:50,333  -->  00:17:54,833
uh by major so uh the overall

403

00:17:55,000  -->  00:18:00,500
the overall uh uh that uh dialectric uh dialectric uh

404

00:18:00,500  -->  00:18:03,366
so overall electrical density it is uh in a

405

00:18:03,366  -->  00:18:07,166
in a July form it is equal to uh ABS not E

406

00:18:07,166  -->  00:18:10,900
and if it is as free space then is epslon R

407

00:18:10,900  -->  00:18:11,966
it is going to be one

408

00:18:11,966  -->  00:18:15,066
then it is the same thing that is your epslon r E

409

00:18:15,166  -->  00:18:19,933
so if the electric field it is in the presence of your

410

00:18:19,933  -->  00:18:22,000
if it is passing to a dialectry

411

00:18:22,000  -->  00:18:24,866
then it will be increased by an amount of this

412

00:18:25,733  -->  00:18:29,200
amount of this uh your polarization factor

413

00:18:29,333  -->  00:18:32,766
and uh further your uh abstinent

414

00:18:32,766  -->  00:18:36,266
it is either it can be defined as a ratio of abstinent

415

00:18:36,266  -->  00:18:37,066
abstinent art

416

00:18:37,366  -->  00:18:41,166
abstinent art that I do permitting and uh an R

417

00:18:41,166  -->  00:18:43,866
it can be defined in terms of the uh

418

00:18:43,866  -->  00:18:45,500
this uh susceptibility

419

00:18:45,500  -->  00:18:47,500
electronic electric susceptibility

420

00:18:47,500  -->  00:18:52,100
uh that is the uh 1+ X E so that has two uh two things

421

00:18:52,100  -->  00:18:54,666
uh two equations for this uh absline R

422

00:18:54,966  -->  00:18:57,666
so the dialectic constrain or relative permitivity

423

00:18:57,666  -->  00:19:00,533
so remember so we also name this epsilon R

424

00:19:00,533  -->  00:19:02,100
as the dialectic constrain

425

00:19:02,100  -->  00:19:05,266
is the ratio of permittivity of dialectic to dialect

426

00:19:05,266  -->  00:19:06,200
free space

427

00:19:07,100  -->  00:19:08,800
here Epstein are

428

00:19:08,800  -->  00:19:14,133
and the sky are dimensionless because they are ratios

429

00:19:14,133  -->  00:19:16,366
and what else

430

00:19:16,966  -->  00:19:19,100
whereas Epstein and Epstein not

431

00:19:19,100  -->  00:19:20,900
we are in Paris by metre

432

00:19:21,666  -->  00:19:23,000
and a dialectic constant

433

00:19:23,000  -->  00:19:24,866
values may change with frequency

434

00:19:24,866  -->  00:19:26,566
so they are functional for frequency

435

00:19:26,566  -->  00:19:28,733
we will study this thing in our common lectures

436

00:19:28,733  -->  00:19:31,033
how they are dependent upon the frequency

437

00:19:31,100  -->  00:19:33,800
and absline r is greater than

438

00:19:34,666  -->  00:19:38,900
Epstein R is always greater than r equal to Trinity

439

00:19:38,900  -->  00:19:41,966
so once it is a free space then Epstein R is equal to 1

440

00:19:41,966  -->  00:19:42,766
and for

441

00:19:43,400  -->  00:19:47,266
and for free space and non dialectic materials

442

00:19:47,266  -->  00:19:48,866
that is your matters your conductors

443

00:19:48,866  -->  00:19:52,466
it is one and for dialectic materials it is

444

00:19:52,566  -->  00:19:54,166
it can be greater than one

445

00:19:56,600  -->  00:19:57,400
what is

446

00:20:12,200  -->  00:20:14,466
when the electric feel in a

447

00:20:14,466  -->  00:20:17,000
in a dialect is sufficiently large

448

00:20:17,000  -->  00:20:19,733
so once we apply an external electric feel

449

00:20:19,733  -->  00:20:22,166
sufficiently large and then what happens it

450

00:20:22,166  -->  00:20:25,300
it it starts to pulling out

451

00:20:25,300  -->  00:20:28,100
electrons out of their molecules

452

00:20:28,266  -->  00:20:30,733
and the dialectic becomes conducting no

453

00:20:30,733  -->  00:20:33,200
so the electrons they know

454

00:20:33,200  -->  00:20:35,200
they are no more stays

455

00:20:35,200  -->  00:20:39,333
bounded under this phenomena of dialectic breakdown

456

00:20:39,333  -->  00:20:42,466
so it is it is converting into a

457

00:20:42,600  -->  00:20:44,466
it is converting into a conductor

458

00:20:44,466  -->  00:20:45,933
like things that the electrons

459

00:20:45,933  -->  00:20:48,333
they are not freely available no

460

00:20:48,333  -->  00:20:51,800
once the externally applied electric release

461

00:20:51,800  -->  00:20:53,400
sufficiently high so that

462

00:20:53,400  -->  00:20:56,200
it can pull out the electrons from extra molecules

463

00:20:56,200  -->  00:20:59,300
and they start moving freely inside the dialectic

464

00:20:59,300  -->  00:21:02,700
so this phenomenon is known as the dialectic plate on

465

00:21:03,300  -->  00:21:06,066
and uh it depends on the nature of the material

466

00:21:06,333  -->  00:21:07,600
uh the temperature

467

00:21:07,600  -->  00:21:09,733
the uh means the environmental condition

468

00:21:09,733  -->  00:21:11,133
the temperature humidity

469

00:21:11,133  -->  00:21:14,200
and the amount of time that we apply the electric fee

470

00:21:15,100  -->  00:21:16,700
and what is the dialector strength

471

00:21:16,700  -->  00:21:18,300
it's the minimum value

472

00:21:18,300  -->  00:21:20,233
it's the minimum value of electric cream

473

00:21:20,300  -->  00:21:23,400
at which electric breakdown occurs

474

00:21:23,966  -->  00:21:25,600
that is known as the dialect strand

475

00:21:25,600  -->  00:21:28,100
of the dialect material or it is

476

00:21:28,100  -->  00:21:29,300
the dialect strand

477

00:21:29,300  -->  00:21:33,600
is the maximum electric field that are dialectic

478

00:21:33,600  -->  00:21:37,866
and target or grid stand without the breakdown

479

00:21:37,866  -->  00:21:40,100
till the time the breakdown has not occurred

480

00:21:41,500  -->  00:21:42,800
so remember

481

00:21:44,600  -->  00:21:49,366
our dielectric is never an IDL diel so it can

482

00:21:49,366  -->  00:21:52,333
it can be converted into a conducting die materials

483

00:21:52,333  -->  00:21:55,900
once we apply the sufficiently large external

484

00:21:55,900  -->  00:21:56,700
electrically

485

00:21:57,400  -->  00:21:57,666
well

486

00:21:57,666  -->  00:22:01,600
let's solve a couple of examples so that it makes you

487

00:22:01,600  -->  00:22:04,233
this topic more clarified

488

00:22:04,266  -->  00:22:07,466
so a dialectric Q of site L

489

00:22:07,466  -->  00:22:10,500
it is centered at the origin and uh

490

00:22:10,500  -->  00:22:14,733
the polarization of H C it is the a r right

491

00:22:14,733  -->  00:22:16,366
it is a constant r r is

492

00:22:16,366  -->  00:22:19,200
we know that it is a position vector

493

00:22:19,200  -->  00:22:21,333
so find all the bound charges

494

00:22:21,333  -->  00:22:23,866
and show that the total bound charges vanishes

495

00:22:25,000  -->  00:22:29,000
let's see here that so is constant over here

496

00:22:29,000  -->  00:22:31,333
remember is constantized your position factor

497

00:22:31,333  -->  00:22:33,733
so for each side so first of all

498

00:22:33,733  -->  00:22:34,500
always remember

499

00:22:34,500  -->  00:22:37,433
you have to plot these things like this right

500

00:22:37,866  -->  00:22:42,266
it is oriented along this

501

00:22:42,266  -->  00:22:45,066
this is your cube like this one right

502

00:22:46,166  -->  00:22:49,000
so let's take the this is your X for example

503

00:22:49,000  -->  00:22:51,100
right and this is your first phase

504

00:22:51,566  -->  00:22:54,433
so you normalize a X in this case right

505

00:22:55,066  -->  00:22:56,400
and that's that's five

506

00:22:56,400  -->  00:22:58,733
that's there are five other phases as well

507

00:22:58,733  -->  00:23:00,533
so total six phases first of all

508

00:23:00,533  -->  00:23:03,133
determine the bounded surface charge

509

00:23:03,133  -->  00:23:06,233
on this first phase different phase you can see

510

00:23:06,333  -->  00:23:09,233
so here since it is centered

511

00:23:09,266  -->  00:23:11,466
centered on the origin

512

00:23:11,466  -->  00:23:15,333
so the front side it will be at the distance of Albi 2

513

00:23:15,333  -->  00:23:17,166
right and the rear

514

00:23:17,166  -->  00:23:20,566
and the rear one will be at the distance of uh

515

00:23:20,566  -->  00:23:22,000
by 2 as well right

516

00:23:22,000  -->  00:23:24,166
and likewise is right hand side

517

00:23:24,333  -->  00:23:25,333
its right hand side

518

00:23:25,333  -->  00:23:28,466
it will be at the distance of Albi 2

519

00:23:28,866  -->  00:23:29,866
and its left hand side

520

00:23:29,866  -->  00:23:32,566
will be also at the distance of Albi 2

521

00:23:33,766  -->  00:23:36,500
okay now let's find out your surface and c

522

00:23:36,500  -->  00:23:37,133
so it is

523

00:23:37,133  -->  00:23:40,533
we know that it is b dot e n and for this front side

524

00:23:40,533  -->  00:23:45,300
this E n is x n uh

525

00:23:45,300  -->  00:23:48,400
for that we also know that this side for this thing

526

00:23:48,400  -->  00:23:52,200
it is x is equal to uh add by two constant

527

00:23:52,600  -->  00:23:53,466
uh no

528

00:23:53,466  -->  00:23:55,066
uh the chart product right

529

00:23:55,066  -->  00:23:57,866
and then we have to evaluate this exit L y 2

530

00:23:57,866  -->  00:24:00,566
so this is your set boundary surface chart identity

531

00:24:00,966  -->  00:24:02,100
uh now the

532

00:24:02,100  -->  00:24:03,366
we educate this thing

533

00:24:03,366  -->  00:24:06,566
so that we can find out the total surface chart

534

00:24:06,566  -->  00:24:10,466
because we have to find out the total charge right

535

00:24:10,566  -->  00:24:11,200
so that with

536

00:24:11,200  -->  00:24:13,700
that is equal to the surplus integral of this

537

00:24:13,700  -->  00:24:15,233
bond with surplus identity

538

00:24:15,766  -->  00:24:18,300
for this surface for the current surface

539

00:24:18,300  -->  00:24:22,400
we know that it is varying with respect to its y and Z

540

00:24:22,466  -->  00:24:24,766
and because the X is constant in this case

541

00:24:24,766  -->  00:24:26,966
that is your L by 2 and the ranges

542

00:24:26,966  -->  00:24:29,866
they are varying from minus L by 2 to L by 2

543

00:24:30,200  -->  00:24:33,500
this thing and 6 we are consuming the 6

544

00:24:33,966  -->  00:24:38,900
6 faces so we multiply the charge of 1

545

00:24:39,766  -->  00:24:42,066
1 surface with 6 so

546

00:24:42,066  -->  00:24:45,566
in order to find a big total charge on all six faces

547

00:24:46,666  -->  00:24:49,333
okay so this is uh Royce

548

00:24:49,333  -->  00:24:51,733
Royce Uhropious it is here by 2

549

00:24:51,733  -->  00:24:54,866
it is coming out as a phone stand and this is the ear

550

00:24:54,866  -->  00:24:57,966
the digital disintegration so it is the area

551

00:24:58,000  -->  00:25:02,333
it is the area of one face that is your L square

552

00:25:02,333  -->  00:25:03,533
L into L L square

553

00:25:03,533  -->  00:25:05,900
so this is your 3 a L Q

554

00:25:06,666  -->  00:25:08,533
let's find out the volume chart text

555

00:25:08,533  -->  00:25:12,566
it is your minus 10 dot b and you measure P

556

00:25:12,566  -->  00:25:16,100
it is in the R you take the dot product of this

557

00:25:16,100  -->  00:25:20,400
so it is simply as it is simply you can take like this

558

00:25:20,400  -->  00:25:22,600
that the take the divergence

559

00:25:22,600  -->  00:25:23,400
take the divergence

560

00:25:23,400  -->  00:25:25,766
so it will be a sum of x plus y plus Z

561

00:25:25,766  -->  00:25:28,200
and we know that X is equal to

562

00:25:29,333  -->  00:25:32,266
X is draining from your constant

563

00:25:32,266  -->  00:25:34,100
so once you take the divergence

564

00:25:34,100  -->  00:25:36,600
with the delevative of x with respect to x is one

565

00:25:36,600  -->  00:25:37,500
delegative of y

566

00:25:37,500  -->  00:25:40,800
respect to y is 1 and then it is 1 + 1 + 1

567

00:25:40,800  -->  00:25:45,366
and then is constant in that 1 + 1 + 1

568

00:25:45,533  -->  00:25:46,966
right and is constant

569

00:25:46,966  -->  00:25:49,000
so it is coming out to be minus 3 8

570

00:25:49,566  -->  00:25:51,666
indicate this over anti volume

571

00:25:51,666  -->  00:25:52,733
for the volume of a q

572

00:25:52,733  -->  00:25:56,566
we know that it is at q if it is equal dimensional

573

00:25:56,566  -->  00:25:58,566
and some of these two charges

574

00:25:58,566  -->  00:25:59,600
total charges

575

00:25:59,800  -->  00:26:03,333
you can appreciate this thing that under polarization

576

00:26:03,333  -->  00:26:07,000
this dialectric is still electrically neutralized

577

00:26:08,700  -->  00:26:10,000
let's solve another example

578

00:26:10,000  -->  00:26:12,300
the electric intensity in a Polish screen

579

00:26:12,333  -->  00:26:14,300
uh is this one

580

00:26:14,400  -->  00:26:18,333
the relative permittivity is given and uh

581

00:26:18,333  -->  00:26:22,066
palaterate capacitor is having the uh

582

00:26:22,066  -->  00:26:23,400
voltage applied across this

583

00:26:23,400  -->  00:26:25,300
it is 10 kilowatt per metres

584

00:26:25,400  -->  00:26:28,200
per metre for the electric intensity is given as a

585

00:26:28,200  -->  00:26:30,466
10 kilowatt per metre if you

586

00:26:30,900  -->  00:26:34,000
and the distance between that plate is 1.5 millimeters

587

00:26:34,000  -->  00:26:36,066
so always take care of these units

588

00:26:36,066  -->  00:26:36,166
now

589

00:26:36,166  -->  00:26:38,700
we need to find out the DP and the surface and bomb

590

00:26:38,700  -->  00:26:40,500
charterance trees and things like this

591

00:26:40,566  -->  00:26:42,200
so let's solve them one by one

592

00:26:42,933  -->  00:26:46,666
so we know that the d the fluxency

593

00:26:46,666  -->  00:26:49,300
it is equal to your absline e

594

00:26:49,300  -->  00:26:52,200
Absline is absline r Absline r

595

00:26:52,266  -->  00:26:54,266
simply solve this equation e

596

00:26:54,266  -->  00:26:56,366
it is 10 kilo watt per meter

597

00:26:56,366  -->  00:26:57,300
so this is your

598

00:26:57,900  -->  00:27:00,900
uh this platter prostitute

599

00:27:00,933  -->  00:27:04,000
uh under the polarization state

600

00:27:05,200  -->  00:27:08,000
for this dialect and what is polarization

601

00:27:08,000  -->  00:27:12,600
polarization it is your Chi epslon r e e e and the sky

602

00:27:12,600  -->  00:27:14,600
it is equal to epslon r minus 1

603

00:27:14,600  -->  00:27:16,700
so all the equation to get its answer

604

00:27:16,733  -->  00:27:19,766
then your P destroys your free

605

00:27:20,366  -->  00:27:22,400
and the question is your free charge

606

00:27:22,500  -->  00:27:27,033
your free charge is d dot E N remember it is d dot E N

607

00:27:28,333  -->  00:27:31,200
and this rope bounded you're bounded

608

00:27:31,200  -->  00:27:35,200
uh bounded surface chart and see it is peed audio right

609

00:27:35,600  -->  00:27:38,900
so you can uh you can find it out that it is basically

610

00:27:38,900  -->  00:27:41,733
it's magnitude it's magnitude uh

611

00:27:41,733  -->  00:27:43,500
because this is also a normal direction

612

00:27:43,500  -->  00:27:44,800
it is also normal direction

613

00:27:44,800  -->  00:27:47,266
so overall it would be the magnitude of the end

614

00:27:47,666  -->  00:27:50,200
and also it will be the magnitude of this P m

615

00:27:50,266  -->  00:27:51,233
the second case

616

00:27:51,733  -->  00:27:54,066
and how to find out the potential between players

617

00:27:54,066  -->  00:27:55,766
this will know that it is called what you need to

618

00:27:55,766  -->  00:27:57,566
d is given is given

619

00:27:57,566  -->  00:27:59,366
so this is your answer for this game

620

00:28:00,933  -->  00:28:02,000
let's follow another example

621

00:28:02,000  -->  00:28:05,100
a dialectic sphere of radius 10 cm

622

00:28:05,100  -->  00:28:06,966
has a point charge of this

623

00:28:07,333  -->  00:28:09,566
centered at it is origin

624

00:28:10,266  -->  00:28:12,666
and uh what we need to calculate the surface

625

00:28:12,666  -->  00:28:14,766
dance to your polarization charge

626

00:28:14,766  -->  00:28:16,833
on the sphere of uh

627

00:28:17,133  -->  00:28:18,400
on the surface of square

628

00:28:18,400  -->  00:28:20,633
before suggested by the charge honour

629

00:28:20,666  -->  00:28:20,933
uh

630

00:28:20,933  -->  00:28:23,733
minus will be cocoon point placed on the sphere of uh

631

00:28:23,733  -->  00:28:24,900
surface of the sphere

632

00:28:25,533  -->  00:28:29,666
learn a solid Azuma point charge is a located region

633

00:28:29,766  -->  00:28:33,100
and the standard equation from

634

00:28:33,100  -->  00:28:35,266
coming out from the cooling star is

635

00:28:35,266  -->  00:28:37,766
Judy Webber for by apslon or scale

636

00:28:37,766  -->  00:28:38,633
no hair

637

00:28:38,700  -->  00:28:42,100
see that the apslon is replaced by absolutely not

638

00:28:42,166  -->  00:28:45,766
we are because here we have the dialect sphere

639

00:28:46,200  -->  00:28:47,866
it's not a free space media

640

00:28:48,666  -->  00:28:49,700
and the second thing

641

00:28:49,700  -->  00:28:51,400
we need to find out the polarization

642

00:28:51,400  -->  00:28:54,066
right and okay

643

00:28:54,066  -->  00:28:57,500
so the polarization we know that it is a Chi epslon r E

644

00:28:57,533  -->  00:29:00,733
simply replace this your hair like

645

00:29:00,733  -->  00:29:03,500
like this one and then epslon R will be cancelled out

646

00:29:03,500  -->  00:29:04,000
so this thing

647

00:29:04,000  -->  00:29:07,333
you have to solve to find out this surface

648

00:29:07,333  -->  00:29:10,933
charge identity under the impact of orization

649

00:29:10,933  -->  00:29:13,500
because it is a p dot a n

650

00:29:13,500  -->  00:29:15,966
and here a n is equal to a r

651

00:29:15,966  -->  00:29:19,366
because things are eminating in the radial direction

652

00:29:19,366  -->  00:29:21,766
for this radical coordinate system

653

00:29:22,166  -->  00:29:24,566
now take the dot order so a dot will be cancer

654

00:29:24,566  -->  00:29:26,366
it will be dotted is equal to 1

655

00:29:26,366  -->  00:29:29,666
and only your left your left to solve this equation

656

00:29:29,666  -->  00:29:32,300
right solve this thing to get this answer

657

00:29:33,600  -->  00:29:35,366
what is force the force between

658

00:29:35,366  -->  00:29:37,066
so force again force again

659

00:29:37,066  -->  00:29:38,700
if I utilize this columns

660

00:29:38,700  -->  00:29:39,200
law

661

00:29:39,200  -->  00:29:42,133
and hold only the differences that you have to replace

662

00:29:42,133  -->  00:29:43,300
this action repeat

663

00:29:43,300  -->  00:29:45,366
Abslan r Abslan R

664

00:29:47,200  -->  00:29:48,000
the last example

665

00:29:48,000  -->  00:29:51,500
find the force with which the players of a parablade

666

00:29:51,933  -->  00:29:53,366
capacitor attract each other

667

00:29:53,366  -->  00:29:56,300
and determine the pressure on the surface of the plate

668

00:29:56,333  -->  00:29:58,566
due to defeat solution

669

00:29:58,566  -->  00:30:00,333
uh from the previous lectures

670

00:30:00,333  -->  00:30:01,666
we know that the electric field

671

00:30:01,666  -->  00:30:05,000
intensity on the surface of each page is uh

672

00:30:05,000  -->  00:30:07,133
R 0 s divided to action E

673

00:30:07,133  -->  00:30:10,433
and right so it is your uh

674

00:30:10,966  -->  00:30:15,033
electric field between uh the two panel plates

675

00:30:16,266  -->  00:30:18,966
okay and where in is the normal to the plate

676

00:30:19,166  -->  00:30:20,800
and so this is the electric

677

00:30:20,800  -->  00:30:23,500
we testing on the surface of one plate right

678

00:30:24,066  -->  00:30:27,300
uh and rice is the surface identity

679

00:30:27,333  -->  00:30:29,200
and we have to find out the force

680

00:30:29,200  -->  00:30:31,500
so that we can find out the pressure uh

681

00:30:31,500  -->  00:30:34,600
so the force is tuned to E to plug in this E

682

00:30:34,600  -->  00:30:35,966
your hair right

683

00:30:35,966  -->  00:30:37,400
your hair and Q

684

00:30:37,400  -->  00:30:40,233
Q will know that you will know that it is

685

00:30:40,900  -->  00:30:43,133
it is D surface chart

686

00:30:43,133  -->  00:30:45,500
and C times the area of that surface

687

00:30:45,500  -->  00:30:47,266
so it is the basic definition

688

00:30:48,166  -->  00:30:51,100
plug in this thing below the SS will be

689

00:30:52,800  -->  00:30:55,266
coming in the numerator right

690

00:30:55,333  -->  00:30:57,300
and then what you can play it on

691

00:30:57,566  -->  00:31:00,000
you can play it on so it is simply fine uh

692

00:31:00,000  -->  00:31:02,166
rosecare to epstonaut so epstonaut here

693

00:31:02,166  -->  00:31:03,833
as you have to use epstonaut

694

00:31:04,400  -->  00:31:06,166
epstonaut you have to replace with epstonaut e

695

00:31:06,166  -->  00:31:08,233
r because it is a dialect

696

00:31:09,800  -->  00:31:13,600
k and in case of a dialectic and

697

00:31:15,133  -->  00:31:17,466
then how you can simplify it further

698

00:31:17,500  -->  00:31:19,066
so you force no

699

00:31:19,066  -->  00:31:20,866
you want you want to find out the force

700

00:31:20,866  -->  00:31:23,500
your force is equal to Q E

701

00:31:24,566  -->  00:31:27,400
right so this is coming out from here

702

00:31:27,400  -->  00:31:28,566
right right here

703

00:31:28,566  -->  00:31:30,566
and then you can simplify like this thing

704

00:31:30,566  -->  00:31:32,500
that you can also write the thing

705

00:31:32,500  -->  00:31:35,533
this role as in terms of your Q as well

706

00:31:35,533  -->  00:31:37,100
so involve the definition of Q

707

00:31:37,100  -->  00:31:39,666
so the expression will be in terms of your Q

708

00:31:39,766  -->  00:31:41,900
so either you write in terms of the charge

709

00:31:41,900  -->  00:31:43,500
or the service chart density

710

00:31:43,500  -->  00:31:44,833
it is the same thing

711

00:31:45,666  -->  00:31:49,000
no pressure so pressure is enforced first unit area

712

00:31:49,000  -->  00:31:52,366
right so this area is going to cancel now

713

00:31:52,366  -->  00:31:54,866
and you will be left out with this pressure term

714

00:31:56,333  -->  00:32:00,600
assignment for your this lecture week No. 8

715

00:32:00,600  -->  00:32:03,266
that is your job to solve these three exam

716

00:32:03,266  -->  00:32:05,133
the three problem exercises

717

00:32:05,133  -->  00:32:07,200
from your second edition of textbook

718

00:32:07,466  -->  00:32:10,566
and you have to submit after the

719

00:32:11,966  -->  00:32:14,400
at the beginning of the next week

720

00:32:14,733  -->  00:32:17,666
after the interactive section for session for this

721

00:32:17,666  -->  00:32:18,800
to lectures

722

00:32:20,266  -->  00:32:21,500
some new previous lectures

723

00:32:21,500  -->  00:32:22,900
so so first of all

724

00:32:22,900  -->  00:32:26,100
we understood what is polarization in the dialectrics

725

00:32:26,100  -->  00:32:26,366
then

726

00:32:26,366  -->  00:32:29,166
how to determine the polarization in the dialectries

727

00:32:29,166  -->  00:32:31,433
and the influence of external lactropine

728

00:32:31,466  -->  00:32:34,866
then we uh we studied what is the dialectic question

729

00:32:34,866  -->  00:32:36,533
and how to determine the

730

00:32:36,533  -->  00:32:38,266
and what is this dialectic strength

731

00:32:38,266  -->  00:32:40,400
and how to determine the dialectic question

732

00:32:40,400  -->  00:32:42,266
of a dialectric

733

00:32:43,533  -->  00:32:44,333
in the next class

734

00:32:44,333  -->  00:32:47,900
we will study some more types of the dialectrics

735

00:32:47,900  -->  00:32:49,100
these are the linear

736

00:32:49,100  -->  00:32:51,400
isotropic and homogeneous dialectics

737

00:32:51,400  -->  00:32:55,166
we will study what is the continuary equation

738

00:32:55,166  -->  00:32:57,966
and how to determine the relaxation time

739

00:32:57,966  -->  00:32:59,633
for the dialectrics

740

00:33:02,166  -->  00:33:05,000
here I thank you all if you have any questions

741

00:33:05,000  -->  00:33:06,500
uh they will be entertained

742

00:33:06,500  -->  00:33:09,100
uh with your emails or online

743

00:33:09,100  -->  00:33:11,566
synchronous sessions that we have arranged

744

00:33:11,566  -->  00:33:12,766
at the department