1 00:00:02,066 --> 00:00:04,933 this is election No. 17 of Amy 2 2 00:00:04,933 --> 00:00:07,300 3 2 Electromagnetic Queen theory 3 00:00:07,400 --> 00:00:11,400 today we will have an overview of question number one 4 00:00:12,266 --> 00:00:17,433 linear isotropic and homogeneous dielectrics properties 5 00:00:17,766 --> 00:00:19,100 continuation 6 00:00:19,100 --> 00:00:23,266 and relaxation time of the dielectric materials 7 00:00:23,966 --> 00:00:27,666 this will cover your sections of 5.7 8 00:00:27,966 --> 00:00:30,100 and 5.8 of your book 9 00:00:30,500 --> 00:00:34,066 and this is academic week No. 10 of your semester 10 00:00:35,400 --> 00:00:37,200 the learning objectives of uh 11 00:00:37,200 --> 00:00:38,966 today's lecture would be 12 00:00:38,966 --> 00:00:41,500 to have an overview of question No. 1 13 00:00:41,500 --> 00:00:42,666 to study linear 14 00:00:42,666 --> 00:00:46,566 isotropic and homogeneous dialect materials 15 00:00:46,566 --> 00:00:49,766 to understand what is continuity equation 16 00:00:49,766 --> 00:00:53,966 and to determine relaxation time inside and uh 17 00:00:53,966 --> 00:00:55,066 dielectric 18 00:00:57,800 --> 00:00:58,966 let's now discuss 19 00:00:58,966 --> 00:01:02,300 some of the properties of these dialect materials 20 00:01:02,800 --> 00:01:06,533 and what technologies we use 21 00:01:06,533 --> 00:01:09,533 once we define these dialectrics 22 00:01:09,533 --> 00:01:10,533 so the first one is 23 00:01:10,533 --> 00:01:14,233 once we see that our material is linear 24 00:01:14,566 --> 00:01:18,000 then it means that d raise 25 00:01:18,000 --> 00:01:20,666 meaningally with respect to e 26 00:01:21,000 --> 00:01:25,500 remember the secretion d is equal to abslon e 27 00:01:25,500 --> 00:01:27,300 the constitute of relationship 28 00:01:27,900 --> 00:01:28,366 so 29 00:01:28,366 --> 00:01:35,300 it says that materials for which action are the Sigma 30 00:01:35,300 --> 00:01:36,500 because for the Sigma 31 00:01:36,500 --> 00:01:39,033 you know that J is equal to Sigma E 32 00:01:39,733 --> 00:01:40,533 right 33 00:01:42,333 --> 00:01:45,600 uh for this uh this type of the materials 34 00:01:45,600 --> 00:01:47,266 uh this outline 35 00:01:47,266 --> 00:01:50,600 or this conductivity does not 36 00:01:50,600 --> 00:01:54,500 re in the region being considered 37 00:01:56,000 --> 00:02:01,233 and this means that they are seen at all times 38 00:02:02,133 --> 00:02:02,866 indeed 39 00:02:02,866 --> 00:02:07,766 3D special partner system and also there that is 40 00:02:07,766 --> 00:02:11,266 you know that it is independent of x 41 00:02:11,266 --> 00:02:13,466 y and z coordinate system 42 00:02:13,566 --> 00:02:17,600 so if it is independent of your geometric 43 00:02:18,266 --> 00:02:20,000 geometrical distribution 44 00:02:20,200 --> 00:02:24,166 then it is going to stay the same toward the 45 00:02:25,200 --> 00:02:29,000 this region and then this material it will 46 00:02:29,000 --> 00:02:32,433 it will be known as the homogeneous meat material 47 00:02:32,566 --> 00:02:34,366 okay so first of all 48 00:02:34,366 --> 00:02:35,500 if the d 49 00:02:35,500 --> 00:02:38,366 it is directly proportional to E inside a material 50 00:02:38,366 --> 00:02:41,000 then if this material is known as the linear 51 00:02:41,066 --> 00:02:44,700 and for that material if this uh 52 00:02:45,266 --> 00:02:47,700 value of this absline dependentivity 53 00:02:47,700 --> 00:02:48,966 and the conductivity 54 00:02:48,966 --> 00:02:52,266 they are going to stay the same throughout the region 55 00:02:52,400 --> 00:02:55,533 and they are independent of the special coordinates 56 00:02:55,533 --> 00:02:55,800 than 57 00:02:55,800 --> 00:02:58,633 their material is known as the homogeneous material 58 00:02:59,100 --> 00:03:00,166 in case 59 00:03:00,933 --> 00:03:02,500 if it is an 60 00:03:02,500 --> 00:03:06,700 in homogeneous or mono homogeneous material 61 00:03:06,800 --> 00:03:09,533 then when this means that 62 00:03:09,533 --> 00:03:13,900 he is dependent upon the space coordinates 63 00:03:14,200 --> 00:03:16,866 and you can take the example of the primativity 64 00:03:16,866 --> 00:03:18,000 of the atmosphere 65 00:03:18,000 --> 00:03:22,233 because it is changing with respect to the altitude 66 00:03:23,600 --> 00:03:24,800 so materials uh 67 00:03:24,800 --> 00:03:27,800 for which it be the electric 68 00:03:27,800 --> 00:03:28,666 first density 69 00:03:28,666 --> 00:03:32,166 and the electric field are in the same direction 70 00:03:32,266 --> 00:03:34,266 are set to be isotropic 71 00:03:34,500 --> 00:03:38,100 so if they are uh in the same direction means that uh 72 00:03:38,300 --> 00:03:38,933 they are well 73 00:03:38,933 --> 00:03:40,666 since we know that they are in their director 74 00:03:40,666 --> 00:03:44,366 quantities and if they are in the same uh directions 75 00:03:44,400 --> 00:03:48,100 uh this means that uh their abslon and Sigma 76 00:03:48,100 --> 00:03:50,700 they are not going to uh raid their 77 00:03:50,700 --> 00:03:52,633 they will stay as the constant 78 00:03:52,733 --> 00:03:53,866 these two things 79 00:03:54,166 --> 00:03:56,133 this thing will be stay at the constant 80 00:03:56,133 --> 00:03:59,200 so this means they are they are in the same direction 81 00:03:59,200 --> 00:04:00,666 and these types of material 82 00:04:00,666 --> 00:04:03,233 they are known as the isotropic materials 83 00:04:03,466 --> 00:04:05,466 and for an isotropic materials 84 00:04:05,466 --> 00:04:07,500 or non isotropic materials 85 00:04:07,700 --> 00:04:10,200 your your this of flux tensity 86 00:04:10,200 --> 00:04:11,266 your lactropine 87 00:04:11,266 --> 00:04:16,933 and polarization are not parallel to this permativity 88 00:04:16,933 --> 00:04:20,000 or this acceptability and in this case 89 00:04:20,000 --> 00:04:22,966 it is going to have the 9 components 90 00:04:23,166 --> 00:04:26,133 because it will vary in all X 91 00:04:26,133 --> 00:04:28,100 y and Z directions 92 00:04:28,966 --> 00:04:33,100 and this variation is referred to as cancer 93 00:04:33,333 --> 00:04:37,200 cancer metrics this thing you can see here 94 00:04:37,466 --> 00:04:39,166 the variation in the x direction 95 00:04:39,166 --> 00:04:41,400 y direction and z direction like this one 96 00:04:41,500 --> 00:04:43,400 duration in the x y direction 97 00:04:43,400 --> 00:04:45,600 duration in x z direction 98 00:04:45,933 --> 00:04:47,700 duration in y z direction 99 00:04:47,700 --> 00:04:50,466 so this combination is going able 100 00:04:50,466 --> 00:04:54,500 reserved in a 9 element metrics 101 00:04:54,666 --> 00:04:56,133 and such a metrics 102 00:04:56,133 --> 00:05:00,066 you can also see that these metrics exhibit 103 00:05:00,066 --> 00:05:03,366 for the crystalline materials 104 00:05:04,000 --> 00:05:06,200 and the magnetized plasma 105 00:05:06,200 --> 00:05:08,300 these these are the two examples 106 00:05:08,300 --> 00:05:10,700 for d and asotropic materials 107 00:05:11,066 --> 00:05:14,066 and here you can see that these components of the d 108 00:05:14,200 --> 00:05:15,766 they are they are 109 00:05:15,766 --> 00:05:19,800 they are not directly proportional to this uh E x 110 00:05:19,800 --> 00:05:23,133 but they are involving this uh 111 00:05:23,133 --> 00:05:27,433 multiplied of this uh radiation terms of the abstract 112 00:05:29,400 --> 00:05:32,800 now summarizing this a dialectic material is linear 113 00:05:32,800 --> 00:05:36,400 if for this d is equal to absent E 114 00:05:36,733 --> 00:05:38,900 the E does not change 115 00:05:39,066 --> 00:05:42,766 once the electric field is applied on that material 116 00:05:42,766 --> 00:05:45,733 so this means that under the influence of external 117 00:05:45,733 --> 00:05:48,633 lactropine the permativity of that material 118 00:05:48,666 --> 00:05:51,700 it is going to steady constant 119 00:05:52,566 --> 00:05:53,666 for dialecting materials 120 00:05:53,666 --> 00:05:57,633 to be qualified as homogeneous materials 121 00:05:57,766 --> 00:06:01,566 uh for this given d 0 absnar not e 122 00:06:01,966 --> 00:06:06,200 e does not change from one point to another point 123 00:06:06,766 --> 00:06:09,133 so this means that your action 124 00:06:09,133 --> 00:06:13,000 it is going to stay constant through this given region 125 00:06:14,500 --> 00:06:17,800 and a dialectromic material is set to be isotropic 126 00:06:17,800 --> 00:06:22,800 if E does not change in different directions 127 00:06:24,533 --> 00:06:27,566 the same idea hose for a connecting materials 128 00:06:27,566 --> 00:06:29,866 for which the home law is applied 129 00:06:29,866 --> 00:06:34,833 that is Jay Z go to absolutely not Jay Z go to Sigma e 130 00:06:35,533 --> 00:06:39,500 and in case uh it is uh linear then uh 131 00:06:39,500 --> 00:06:41,100 your stigma does not uh 132 00:06:41,333 --> 00:06:43,600 change once the electricity supply 133 00:06:43,733 --> 00:06:45,666 and if it is homogeneous then 134 00:06:45,666 --> 00:06:47,666 stigma is going to stay constant 135 00:06:47,666 --> 00:06:49,633 at all the points in the region 136 00:06:49,733 --> 00:06:52,600 and if it is isotropic then stigma 137 00:06:52,800 --> 00:06:53,566 the conductivity 138 00:06:53,566 --> 00:06:56,466 does not vary with respect to direction in the 139 00:06:56,700 --> 00:06:59,466 and different directions 140 00:07:01,300 --> 00:07:03,233 so for linear 141 00:07:03,366 --> 00:07:08,066 isotropic and homogeneous media are formulas 142 00:07:09,666 --> 00:07:11,500 dried for free space 143 00:07:11,766 --> 00:07:15,700 can be applied for these types of demetrial 144 00:07:15,700 --> 00:07:17,266 which are linear isotropic 145 00:07:17,266 --> 00:07:18,433 and homogeneous 146 00:07:18,733 --> 00:07:23,766 by simply replacing the abslanaut with this abslanaut 147 00:07:23,766 --> 00:07:29,033 abslanaut are abslineaut into Abslineaut I 148 00:07:29,066 --> 00:07:32,500 and we know that this is all equal to simply be 149 00:07:32,533 --> 00:07:34,166 abstinaut abstlont 150 00:07:34,533 --> 00:07:38,933 so the simple thing is if it is a cooling star only 151 00:07:38,933 --> 00:07:39,800 you have to replay 152 00:07:39,800 --> 00:07:43,466 this actual knot is equal to absolute knot 153 00:07:43,500 --> 00:07:44,866 absna RD 154 00:07:45,400 --> 00:07:47,400 the product of this optional knot 155 00:07:47,400 --> 00:07:50,766 and the relative permittivity of that medium 156 00:07:51,766 --> 00:07:53,400 and for the similarly on the 157 00:07:53,400 --> 00:07:55,100 all the previous formulas 158 00:07:55,100 --> 00:07:58,000 you have to replace this abstlon 159 00:07:58,000 --> 00:08:00,766 knot with this abstlon 160 00:08:00,800 --> 00:08:03,933 which is equal to this abstlon knot into the 161 00:08:03,933 --> 00:08:06,833 a relative primativity of that but the medium 162 00:08:09,200 --> 00:08:12,166 let's say discuss what is this continuity question 163 00:08:12,166 --> 00:08:14,633 and what is this relaxation time 164 00:08:14,866 --> 00:08:17,100 so uh we know that 165 00:08:17,100 --> 00:08:21,033 due to the principle of charge conservation 166 00:08:21,533 --> 00:08:25,700 the time rate of decrease of charge 167 00:08:25,766 --> 00:08:27,300 within a given volume 168 00:08:28,266 --> 00:08:30,133 within a given volume so the 169 00:08:30,133 --> 00:08:32,266 it is uh you know it is at decrease 170 00:08:32,266 --> 00:08:35,900 so it is represented as the negative quantity 171 00:08:36,066 --> 00:08:40,233 so it is at decrease in the rate of change of this uh 172 00:08:41,000 --> 00:08:44,500 this charge with respect to time inside the volume 173 00:08:44,866 --> 00:08:50,266 and it is equal to the net outward current 174 00:08:50,266 --> 00:08:52,600 flowing to that close surface 175 00:08:52,800 --> 00:08:55,866 so that is a definition so we know that the current 176 00:08:55,866 --> 00:08:58,800 it is equal to date of change of the charge 177 00:08:58,866 --> 00:09:00,466 with respect to time 178 00:09:00,466 --> 00:09:03,400 and if it is decreasing inside the 179 00:09:03,566 --> 00:09:05,666 if you charge it decreasing inside of warning 180 00:09:05,666 --> 00:09:07,766 then it will be termed as a minus term 181 00:09:07,866 --> 00:09:12,566 and from this um uh if we are given the 182 00:09:12,800 --> 00:09:13,633 this uh 183 00:09:14,400 --> 00:09:17,200 this electric condensity information 184 00:09:17,200 --> 00:09:19,866 and we evaluate the closing trigger of this 185 00:09:19,866 --> 00:09:21,266 electric condensity 186 00:09:21,300 --> 00:09:24,266 with respect to this surface element 187 00:09:24,266 --> 00:09:26,700 that it also gives out this uh 188 00:09:26,700 --> 00:09:29,200 current coming out of that close surface 189 00:09:29,200 --> 00:09:33,266 so that is the definition of this uh current 190 00:09:33,733 --> 00:09:36,400 so where in this uh definition q in 191 00:09:36,400 --> 00:09:37,900 Q in is the total chart 192 00:09:37,900 --> 00:09:41,266 which was residing inside this closed surface 193 00:09:41,266 --> 00:09:43,566 and it is decreasing respect to time 194 00:09:44,666 --> 00:09:46,933 let's simplify the things we know 195 00:09:46,933 --> 00:09:49,366 that q it is equal to the volume 196 00:09:49,366 --> 00:09:52,066 tribular of the volume chart density 197 00:09:52,500 --> 00:09:55,366 and we can change this to operators 198 00:09:55,366 --> 00:09:57,466 the linear operators of the integration 199 00:09:57,466 --> 00:09:58,700 and the differentiation 200 00:09:59,900 --> 00:10:01,900 and let's apply this uh 201 00:10:01,900 --> 00:10:06,266 divergent here on this first term right 202 00:10:06,333 --> 00:10:09,600 uh so this uh you can uh you can solve this digit 203 00:10:09,600 --> 00:10:10,366 it is closed 204 00:10:10,366 --> 00:10:13,333 in circumstances that it is equal to the open volume 205 00:10:13,333 --> 00:10:16,266 table of the divergence of this human factor quantity 206 00:10:16,533 --> 00:10:20,066 and from this so you can wear with this volume trigger 207 00:10:20,500 --> 00:10:22,433 and this volume trigger 208 00:10:22,733 --> 00:10:24,866 and then these two volume triggers 209 00:10:24,866 --> 00:10:26,500 they are going to cancel out 210 00:10:26,500 --> 00:10:28,900 and you're going to laptop with this uh 211 00:10:28,900 --> 00:10:32,500 divergents of this electric uh credensity 212 00:10:33,366 --> 00:10:36,666 uh is related with 213 00:10:37,900 --> 00:10:40,833 the rate of change of this wall in identity 214 00:10:41,266 --> 00:10:44,266 it decrease in rate of change of this wall of identity 215 00:10:44,300 --> 00:10:44,533 and 216 00:10:44,533 --> 00:10:49,100 this equation is known as the continuity of current 217 00:10:49,100 --> 00:10:52,400 equation or the continent equation 218 00:10:53,366 --> 00:10:55,066 so it states that 219 00:10:56,333 --> 00:11:01,766 it states that uh it is derived from the principle of 220 00:11:01,766 --> 00:11:04,433 conservation of charge and it states that 221 00:11:04,500 --> 00:11:08,966 there can be no accumulation of charge 222 00:11:09,533 --> 00:11:12,700 at any point inside that given volume 223 00:11:12,700 --> 00:11:14,466 so in this particular example 224 00:11:14,466 --> 00:11:16,800 it is going to decrease in this case 225 00:11:16,800 --> 00:11:19,200 because the neck current 226 00:11:19,200 --> 00:11:23,866 it is going outside of this closed surface 227 00:11:25,200 --> 00:11:26,866 so for steady state plans 228 00:11:26,866 --> 00:11:29,800 we know that there's no rate of change of this uh 229 00:11:30,133 --> 00:11:33,200 volume identity has from Continental Christian 230 00:11:33,266 --> 00:11:35,400 this ten dot g is equal to zero 231 00:11:35,466 --> 00:11:38,300 showing that the total charge 232 00:11:38,300 --> 00:11:39,400 leaving a volume 233 00:11:39,400 --> 00:11:42,866 is seen as the total charge entering it 234 00:11:42,866 --> 00:11:45,700 so there's no divergence in this case 235 00:11:47,266 --> 00:11:50,533 and uh also it is all the equency of your 236 00:11:50,533 --> 00:11:52,500 uh controls uh 237 00:11:52,500 --> 00:11:55,400 current law that at one particular node 238 00:11:55,566 --> 00:11:58,866 the current entering is equal to the current living 239 00:11:58,966 --> 00:12:00,733 and in this key in this also 240 00:12:00,733 --> 00:12:02,633 uh also the case of this uh 241 00:12:03,266 --> 00:12:06,100 close surface if it's the close surface 242 00:12:06,100 --> 00:12:11,800 the current entry in is equal to the current out 243 00:12:11,966 --> 00:12:15,600 then there will be no flux outside of this 244 00:12:16,700 --> 00:12:20,600 outside of this complete close surface 245 00:12:22,300 --> 00:12:24,266 so consider introducing a charge 246 00:12:24,266 --> 00:12:26,500 let's let's introduce a charge inside this 247 00:12:26,500 --> 00:12:28,200 uh at close volume 248 00:12:28,200 --> 00:12:29,800 okay and uh 249 00:12:29,800 --> 00:12:32,800 from this uh we know that 250 00:12:42,500 --> 00:12:45,400 uh I think the constituted relationship 251 00:12:45,533 --> 00:12:48,733 b is equal to ABS or not e as del dot e 252 00:12:48,733 --> 00:12:51,600 it is equal to will be directed ABS or not and not 253 00:12:51,600 --> 00:12:53,833 let's substitute the continuity question 254 00:12:55,900 --> 00:13:01,066 how to substitute 255 00:13:03,933 --> 00:13:05,366 and first of all 256 00:13:05,366 --> 00:13:08,900 substitute this on vibration into this causes bar 257 00:13:08,900 --> 00:13:13,366 so we have this thing and from here 258 00:13:14,733 --> 00:13:17,866 uh from here what we can assume things 259 00:13:18,000 --> 00:13:21,033 okay from here right 260 00:13:21,466 --> 00:13:25,166 put this Del dot J inside this continent equation 261 00:13:25,166 --> 00:13:29,700 the arms are inside this continent equation and then uh 262 00:13:29,700 --> 00:13:32,833 you can uh further simplify the things 263 00:13:33,500 --> 00:13:34,900 so okay 264 00:13:36,100 --> 00:13:37,333 uh okay 265 00:13:37,333 --> 00:13:40,600 so what is this uh you have to 266 00:13:42,133 --> 00:13:43,000 uh okay 267 00:13:43,000 --> 00:13:46,600 so their dark G it was equal to minus rate of change 268 00:13:46,600 --> 00:13:48,200 of describing identity 269 00:13:48,266 --> 00:13:53,000 so J's from onside is equal to Sigma E 270 00:13:54,333 --> 00:13:58,166 and uh let's plug in other things okay 271 00:13:58,166 --> 00:14:00,500 so Sigma is coming out as a question 272 00:14:00,666 --> 00:14:04,366 so your dial dot e it is equal to 273 00:14:05,700 --> 00:14:09,400 will be divided by absent from this cause as well okay 274 00:14:09,966 --> 00:14:12,200 but if you rearrange this equation 275 00:14:12,200 --> 00:14:17,566 you will find out that it is homogeneous linear 276 00:14:18,333 --> 00:14:20,566 first charter differential equation 277 00:14:20,666 --> 00:14:21,100 and all 278 00:14:21,100 --> 00:14:23,666 herit is known as the ordinary differential equation 279 00:14:23,666 --> 00:14:26,666 because it is a first charter differential equation 280 00:14:27,366 --> 00:14:28,833 when I solve this equation 281 00:14:30,066 --> 00:14:34,100 since uh it can be uh it can be swallowed 282 00:14:34,100 --> 00:14:37,966 using this technique of separating the variables 283 00:14:37,966 --> 00:14:40,933 so take the variables of this uh 284 00:14:40,933 --> 00:14:43,766 Ruby on one side and the uh 285 00:14:43,766 --> 00:14:46,766 this uh radio belt of this uh 286 00:14:47,200 --> 00:14:49,233 time term on the second side 287 00:14:49,366 --> 00:14:50,933 integrate both sides 288 00:14:50,933 --> 00:14:53,966 so uh integration of this thing right 289 00:14:53,966 --> 00:14:57,200 integration of this thing with respect to Rovi 290 00:14:57,466 --> 00:15:00,266 so integration of one of a Rovi with respect to Rovi 291 00:15:00,266 --> 00:15:03,100 it is we know that Eleanor Rovi 292 00:15:03,566 --> 00:15:06,700 because you know that integration of one of our X 293 00:15:06,933 --> 00:15:10,766 it was equal to I don't know facts right 294 00:15:10,766 --> 00:15:13,566 so remember these things from your future point 295 00:15:13,566 --> 00:15:15,800 uh problem solving as well 296 00:15:17,566 --> 00:15:19,600 integrational constant with respect to t 297 00:15:19,600 --> 00:15:26,566 it is t and how to get this construct of integration c 298 00:15:26,700 --> 00:15:30,200 right we know that at t is equal to 0 299 00:15:30,700 --> 00:15:32,200 at t is equal to zero 300 00:15:33,166 --> 00:15:38,466 your will be it is equal to will we not 301 00:15:38,966 --> 00:15:40,166 so plug in this failure 302 00:15:40,166 --> 00:15:42,066 you will find out that this constant 303 00:15:42,066 --> 00:15:45,166 it is equal to Eleanor will we not 304 00:15:45,900 --> 00:15:48,000 so let's simplify this term 305 00:15:49,166 --> 00:15:52,133 uh okay these two are Ellen terms 306 00:15:52,133 --> 00:15:54,000 so bring this Ellen term over here 307 00:15:54,000 --> 00:15:56,366 so Ellen of uh will be 308 00:15:57,733 --> 00:16:02,400 minus Eleanor will be not 309 00:16:02,900 --> 00:16:06,766 we know that the subtraction of Ellen terms 310 00:16:06,766 --> 00:16:08,033 it is equal to the 311 00:16:10,500 --> 00:16:14,466 division of these two the 312 00:16:15,733 --> 00:16:17,533 division of these two terms 313 00:16:17,533 --> 00:16:20,766 and then you can you can take the natural lower 314 00:16:20,766 --> 00:16:22,733 lower technique of these two terms 315 00:16:22,733 --> 00:16:24,166 so that relationship 316 00:16:24,166 --> 00:16:26,366 you know from your elementary maths 317 00:16:27,366 --> 00:16:30,866 okay and how to fully simplify 318 00:16:30,900 --> 00:16:32,933 so take the anti lower both sides 319 00:16:32,933 --> 00:16:35,100 so once you will take the anti lower both sides 320 00:16:35,100 --> 00:16:38,566 you will left over with this will be divided by 321 00:16:39,666 --> 00:16:40,766 will be not 322 00:16:42,066 --> 00:16:43,333 and on the right hand side 323 00:16:43,333 --> 00:16:47,066 the whole thing which was optional 324 00:16:47,100 --> 00:16:50,800 which was this exponential risk from minus t 325 00:16:50,800 --> 00:16:56,733 divided by minus t in two row divided by this signal 326 00:16:56,733 --> 00:16:58,100 divided by abslon 327 00:16:59,100 --> 00:17:02,400 when this term signal divided by abslon 328 00:17:02,400 --> 00:17:05,066 it can be defined as Dr 329 00:17:05,533 --> 00:17:08,266 and this this is known as the time construct as well 330 00:17:08,333 --> 00:17:10,266 and I'll try to able to see that 331 00:17:10,266 --> 00:17:12,900 it is also relaxation time as well 332 00:17:14,066 --> 00:17:16,766 so once you take the engine over both sides 333 00:17:16,766 --> 00:17:18,133 you can simplify these terms 334 00:17:18,133 --> 00:17:24,433 so this is this is a exponentially decaying expression 335 00:17:24,600 --> 00:17:26,000 so so 336 00:17:26,000 --> 00:17:28,066 this is your starting charge 337 00:17:28,066 --> 00:17:30,100 inside your clothes region 338 00:17:30,366 --> 00:17:32,966 and it is decaying exponentially 339 00:17:32,966 --> 00:17:34,900 with respect to this factor 340 00:17:35,366 --> 00:17:39,166 and since it is decaying so here this TR 341 00:17:39,733 --> 00:17:41,666 it is at time constant thing 342 00:17:42,300 --> 00:17:44,233 and it is defined in these seconds 343 00:17:44,566 --> 00:17:47,166 and further it is equal to absline 344 00:17:47,166 --> 00:17:49,800 divided by this Sigma of that vertical medium 345 00:17:51,400 --> 00:17:53,900 so once we introduce that 1 346 00:17:53,900 --> 00:17:56,600 inchar density at the interior 347 00:17:56,600 --> 00:17:59,000 inside a material it will decay 348 00:17:59,066 --> 00:18:00,466 resulting in the chart 349 00:18:00,466 --> 00:18:03,700 movement from the interior point at 350 00:18:03,700 --> 00:18:05,900 at which it was introduced 351 00:18:05,933 --> 00:18:07,700 to the surface of the material 352 00:18:08,366 --> 00:18:11,333 and the time constant TR or the decay 353 00:18:11,333 --> 00:18:13,300 it is known as relaxation time 354 00:18:13,300 --> 00:18:15,033 or the rearrangement time 355 00:18:15,200 --> 00:18:18,366 but the charge is moving toward the surface of that 356 00:18:18,966 --> 00:18:21,466 material that dialect material 357 00:18:21,866 --> 00:18:25,600 and it is also defined as relaxation time 358 00:18:25,600 --> 00:18:30,600 is the time it is for a charge please 359 00:18:32,200 --> 00:18:35,833 in the interior of the material to draw to E 360 00:18:36,100 --> 00:18:38,600 raise to power minus 1 and as we solve it 361 00:18:38,600 --> 00:18:44,566 it is equal to 36 6.8% of this initial value 362 00:18:44,866 --> 00:18:48,433 so the relaxation time is a time in which 363 00:18:49,533 --> 00:18:51,933 so once you will put that t is equal to t 364 00:18:51,933 --> 00:18:53,500 r in the expression 365 00:18:54,100 --> 00:18:55,733 so basically t r 366 00:18:55,733 --> 00:18:58,966 is a time after which 367 00:18:58,966 --> 00:19:04,300 only 36.5% of the initial charge will be left 368 00:19:04,300 --> 00:19:07,800 inside that material 369 00:19:08,466 --> 00:19:12,066 if this will be not is placed 370 00:19:12,066 --> 00:19:16,666 placed inside that material so uh 371 00:19:16,666 --> 00:19:18,366 it is very short for uh 372 00:19:18,366 --> 00:19:22,366 for good conductor and very long for good dialectry 373 00:19:22,400 --> 00:19:24,866 let's see the example for a good conductor 374 00:19:24,866 --> 00:19:27,533 the relaxation time is so short 375 00:19:27,533 --> 00:19:27,766 that 376 00:19:27,766 --> 00:19:31,566 most of the charge will vanish from the interior point 377 00:19:31,566 --> 00:19:35,066 and immediately appear at the surface 378 00:19:36,333 --> 00:19:36,966 within a very 379 00:19:36,966 --> 00:19:42,133 short time because the conductivity of this uh 380 00:19:42,133 --> 00:19:44,166 these conductors for example the cover 381 00:19:44,166 --> 00:19:47,100 it is very high so once you you saw this 382 00:19:47,100 --> 00:19:48,066 we know that developing 383 00:19:48,066 --> 00:19:51,566 permitting of of the conductor it is equal to 1 384 00:19:51,566 --> 00:19:54,566 so for this t r relaxation time 385 00:19:54,566 --> 00:19:58,433 it is equal to Absline R into Absline R 386 00:19:58,533 --> 00:19:59,900 there are the stigma 387 00:19:59,900 --> 00:20:03,100 so it is coming out to be tenders from minus 19 388 00:20:03,100 --> 00:20:04,333 which is very very small 389 00:20:04,333 --> 00:20:05,866 small time 390 00:20:06,966 --> 00:20:08,600 there is for a good dialect 391 00:20:08,600 --> 00:20:10,400 relaxation time is very long 392 00:20:10,400 --> 00:20:11,500 once the charge 393 00:20:11,500 --> 00:20:14,800 it is introduced at the centre of this dialect 394 00:20:15,000 --> 00:20:18,200 it remains wherever it is 395 00:20:18,200 --> 00:20:20,966 pays for times maybe up to days 396 00:20:21,100 --> 00:20:23,366 so the king is very small in this case 397 00:20:24,266 --> 00:20:27,133 uh because the connectivity is very small 398 00:20:27,133 --> 00:20:32,400 temperature minus 17 optional for this uh quads uh 399 00:20:34,466 --> 00:20:35,166 dialect 400 00:20:35,166 --> 00:20:39,833 it is five to solve this expression for this dialect 401 00:20:40,333 --> 00:20:44,666 and you can see that it is 51 point two days 402 00:20:44,866 --> 00:20:47,566 so after 51.2 days 403 00:20:47,800 --> 00:20:51,133 the inserted charge inside the dialectic 404 00:20:51,133 --> 00:20:57,700 it will decay to 36 point uh as uh that uh 8 person 405 00:21:00,600 --> 00:21:02,133 summing up today's lecture 406 00:21:02,133 --> 00:21:05,100 so today we had an overview of your question No. 1 407 00:21:05,200 --> 00:21:06,600 we studied what is linear 408 00:21:06,600 --> 00:21:09,533 isotropic and homogeneous dialectrics 409 00:21:09,533 --> 00:21:12,166 we understood what is continental equation 410 00:21:12,166 --> 00:21:15,133 and how it is utilized to determine the relaxation 411 00:21:15,133 --> 00:21:17,666 timer are a dialectic 412 00:21:18,466 --> 00:21:19,100 next time 413 00:21:19,100 --> 00:21:21,866 we're going to study very important topic of your 414 00:21:21,866 --> 00:21:26,200 uh electrostatic that is the electric Bondi condition 415 00:21:26,200 --> 00:21:29,400 that what happens once an electric field 416 00:21:29,400 --> 00:21:33,733 it moves it travels from one medium to another medium 417 00:21:33,733 --> 00:21:36,433 with different dialectic properties 418 00:21:39,166 --> 00:21:40,400 here I thank you all 419 00:21:40,400 --> 00:21:42,000 if you have any questions 420 00:21:42,000 --> 00:21:43,533 uh they will be entertained 421 00:21:43,533 --> 00:21:46,100 uh through your emails or online 422 00:21:46,100 --> 00:21:47,200 synchronous sessions 423 00:21:47,200 --> 00:21:49,766 that we have arranged at the department