1 00:00:01,800 --> 00:00:04,900 this is election No. 18 of baby 2 2 00:00:04,900 --> 00:00:08,566 3 2 electromagnetic field theory 3 00:00:08,766 --> 00:00:09,800 today uh 4 00:00:09,800 --> 00:00:13,200 we will study electric field bound conditions 5 00:00:13,300 --> 00:00:17,666 and this will cover your section 5.9 of textbook 6 00:00:19,866 --> 00:00:23,466 the learning objectives of today's lecture would be 7 00:00:24,733 --> 00:00:28,466 what are electric field boundary conditions 8 00:00:29,600 --> 00:00:33,166 and uh what is the impact of uh 9 00:00:33,333 --> 00:00:36,166 dialective to dialective boundary conditions 10 00:00:36,166 --> 00:00:38,666 on the travelling of electric fee 11 00:00:38,666 --> 00:00:40,433 from one medium to another 12 00:00:40,866 --> 00:00:42,266 and likewise 13 00:00:42,366 --> 00:00:46,266 the dependency upon this conductor to dielectric 14 00:00:46,266 --> 00:00:47,566 boundary conditions 15 00:00:47,566 --> 00:00:51,966 and conductor to free space of boundary conditions 16 00:00:51,966 --> 00:00:55,566 upon the traveling of this electric field 17 00:00:55,566 --> 00:00:57,466 from one medium to another 18 00:00:59,200 --> 00:01:01,466 first of all the boundary conditions 19 00:01:01,966 --> 00:01:03,266 once uh 20 00:01:03,266 --> 00:01:06,233 the field exist in a medium 21 00:01:06,466 --> 00:01:09,133 which is for the consisting of uh 22 00:01:09,133 --> 00:01:11,400 two different media uh 23 00:01:11,400 --> 00:01:13,500 and the properties of these two 24 00:01:13,500 --> 00:01:16,733 dialectic properties of these two materials 25 00:01:16,733 --> 00:01:18,800 they are uh different 26 00:01:18,933 --> 00:01:21,966 then these are the conditions upon 27 00:01:21,966 --> 00:01:23,000 the conditions are 28 00:01:23,000 --> 00:01:28,266 the conditions that the electric feed must specify 29 00:01:29,166 --> 00:01:32,700 at the interface of these two sexes 30 00:01:32,800 --> 00:01:35,433 at the boundaries of these two sexes 31 00:01:35,733 --> 00:01:37,900 and that's why they are known as 32 00:01:37,900 --> 00:01:39,300 the boundary conditions so 33 00:01:39,300 --> 00:01:42,866 these are the conditions that for this particular case 34 00:01:42,866 --> 00:01:45,433 the electric feed must 35 00:01:47,500 --> 00:01:54,400 satisfy and the interface between these two medium 36 00:01:55,266 --> 00:01:57,100 so for electrostatic feed 37 00:01:57,300 --> 00:01:59,900 uh we will consider following boundary conditions 38 00:01:59,900 --> 00:02:02,166 which allow most importance 39 00:02:02,400 --> 00:02:05,266 uh the dialector to dialectric interface 40 00:02:05,266 --> 00:02:07,400 the conductor to dialectic interface 41 00:02:07,700 --> 00:02:10,466 and the conductor to freespace interface 42 00:02:11,900 --> 00:02:16,766 I know that they are always helpful in determining uh 43 00:02:16,766 --> 00:02:20,200 the field on one side of the boundary 44 00:02:20,466 --> 00:02:24,900 if we have the knowledge of electric field 45 00:02:24,933 --> 00:02:27,833 on the other side of the boundary 46 00:02:27,866 --> 00:02:30,466 so if we know the field on one side of the boundary 47 00:02:30,466 --> 00:02:32,166 then we can the remain 48 00:02:32,166 --> 00:02:34,900 the electric field on the other side of the boundary 49 00:02:34,900 --> 00:02:39,166 so that is the significance of the boundary conditions 50 00:02:41,133 --> 00:02:44,200 and uh in order to drive these boundary conditions 51 00:02:44,200 --> 00:02:47,366 we make sure that the maximum equation uh 52 00:02:47,366 --> 00:02:51,866 the maximum equation 1 and 2 that we drive for this uh 53 00:02:52,133 --> 00:02:53,966 uh that is your closing tirular 54 00:02:53,966 --> 00:02:56,700 electrostatic field around the closed part 55 00:02:56,700 --> 00:03:00,566 it is uh equal to zero and that is your electric field 56 00:03:00,566 --> 00:03:04,666 it is uh you know that it is uh conservated 57 00:03:04,666 --> 00:03:07,666 yeah uh uh electroconturity 58 00:03:08,066 --> 00:03:10,333 and the second one is your uh 59 00:03:10,333 --> 00:03:15,200 is your uh that uh gaze is yeah gaze is gaze is clear 60 00:03:16,500 --> 00:03:20,066 that the charge and closed uh is equal to the flex 61 00:03:20,066 --> 00:03:23,400 uh passing to that uh close surface 62 00:03:24,166 --> 00:03:26,900 and we will also make sure of this uh 63 00:03:26,900 --> 00:03:29,500 decomposition of electric uh 64 00:03:29,700 --> 00:03:33,733 feed and electric first density into two autobinal uh 65 00:03:33,733 --> 00:03:34,766 components 66 00:03:35,366 --> 00:03:39,466 uh that is your potential and your normal components 67 00:03:39,800 --> 00:03:42,166 potential and your normal components 68 00:03:43,300 --> 00:03:45,066 and we were also majors of this 69 00:03:45,066 --> 00:03:48,400 constituted relationship between this electric feed 70 00:03:48,400 --> 00:03:50,800 and the electric feed dynasty 71 00:03:52,166 --> 00:03:56,700 let's have this first born recognition that is 72 00:04:00,100 --> 00:04:00,900 medium 73 00:04:01,666 --> 00:04:04,300 so consider the boundary between two dialectic 74 00:04:04,300 --> 00:04:05,866 with permittivities ABS 1 75 00:04:05,866 --> 00:04:07,200 1 and ABS 1 2 76 00:04:07,200 --> 00:04:08,833 we know that uh 77 00:04:08,933 --> 00:04:11,000 uh if they are other than the free space 78 00:04:11,000 --> 00:04:14,066 they will be expressed in terms of their relative 79 00:04:14,066 --> 00:04:16,866 permittivity multiplied with the 80 00:04:17,400 --> 00:04:19,433 by mittility of the free space 81 00:04:19,933 --> 00:04:21,400 so these are the two medium 82 00:04:21,933 --> 00:04:23,400 your electric field 83 00:04:23,400 --> 00:04:27,966 it is moving from medium 2 to medium 1 in this case 84 00:04:29,466 --> 00:04:34,766 and uh or in the medium 1 we're having this uh 85 00:04:34,766 --> 00:04:37,166 electrical 1 in the medium 2 86 00:04:37,166 --> 00:04:39,266 we're having this electrical 2 87 00:04:39,266 --> 00:04:41,333 which are further having the tenantial 88 00:04:41,333 --> 00:04:45,233 and the normal components as express chair 89 00:04:46,600 --> 00:04:52,166 when I solve this uh post uh maximum equation 90 00:04:53,333 --> 00:04:56,133 uh that is your close in check it off line in 91 00:04:56,133 --> 00:05:00,100 check it off electric field around disclosed park a B 92 00:05:00,100 --> 00:05:00,600 C G 93 00:05:00,600 --> 00:05:02,000 a in the given figure 94 00:05:02,733 --> 00:05:03,700 and so in this case 95 00:05:03,700 --> 00:05:06,733 we are assuming this close part that is a B 96 00:05:06,733 --> 00:05:08,666 C G right 97 00:05:08,666 --> 00:05:11,900 now let's solve this integration around this close part 98 00:05:13,000 --> 00:05:13,800 right 99 00:05:15,500 --> 00:05:19,500 and uh for this uh according to this medium 100 00:05:19,500 --> 00:05:19,900 uh 101 00:05:19,900 --> 00:05:23,066 we would take this uh financial and normal conference 102 00:05:23,533 --> 00:05:25,866 so let's start from this this a to B 103 00:05:26,800 --> 00:05:31,600 for this a to B we only have this in this medium one 104 00:05:31,600 --> 00:05:33,900 we have this E1T 105 00:05:34,500 --> 00:05:36,400 right it's initial component 106 00:05:36,766 --> 00:05:39,333 and what is the length of this path 107 00:05:39,333 --> 00:05:42,266 that is JTW right 108 00:05:43,200 --> 00:05:45,566 okay for this segment that is your 109 00:05:45,566 --> 00:05:49,633 uh B to uh B to that uh interface 110 00:05:50,500 --> 00:05:54,266 you have this e 1 n but it is in B 111 00:05:55,733 --> 00:05:58,500 it is in B opposite direction as to B 112 00:06:00,000 --> 00:06:02,900 so it is in the upper direction right 113 00:06:03,100 --> 00:06:07,566 even n it is in the upper direction and this uh your 114 00:06:08,933 --> 00:06:13,633 direction of motion into this circulation part 115 00:06:13,800 --> 00:06:15,800 it is in the clockwise direction 116 00:06:15,800 --> 00:06:18,000 whereas the normal it is B 117 00:06:18,000 --> 00:06:20,266 it is in the upper direction right 118 00:06:20,866 --> 00:06:24,666 so that's why it is going to have this minus sign 119 00:06:24,666 --> 00:06:26,633 because the data it is equal to 120 00:06:28,266 --> 00:06:31,800 one 80 degree and we know that call of one 80 degree 121 00:06:31,800 --> 00:06:33,600 it is equal to minus 1 122 00:06:34,300 --> 00:06:38,200 okay for the second part uh uh that is 123 00:06:38,200 --> 00:06:39,666 so for this part this 124 00:06:39,666 --> 00:06:43,200 the differential land is equal to del 125 00:06:43,200 --> 00:06:44,866 age divided by two 126 00:06:46,000 --> 00:06:50,200 and also for this one this is dial age divided by 2 127 00:06:50,300 --> 00:06:51,900 but the only difference is 128 00:06:52,266 --> 00:06:52,666 you know 129 00:06:52,666 --> 00:06:57,133 you are in the region 2 and you're having this E to 130 00:06:57,133 --> 00:06:59,066 and normal component again 131 00:06:59,066 --> 00:07:01,200 the direction is in the opposite direction 132 00:07:01,600 --> 00:07:03,300 to this circulation part 133 00:07:03,533 --> 00:07:06,100 that's why you are going to have this minus sign 134 00:07:06,700 --> 00:07:07,766 and for this 135 00:07:09,100 --> 00:07:13,300 length segment that is from C to D your turn is 136 00:07:13,300 --> 00:07:14,966 you are in the second medium right 137 00:07:15,000 --> 00:07:16,966 so your turn is your component 138 00:07:16,966 --> 00:07:19,200 it is E2T 139 00:07:19,266 --> 00:07:22,800 it is in the opposite direction to this circulation 140 00:07:22,800 --> 00:07:23,266 pass so 141 00:07:23,266 --> 00:07:25,866 that's why you are again going to have this minus sign 142 00:07:27,000 --> 00:07:30,866 now for this normal component in this uh region two 143 00:07:31,000 --> 00:07:32,466 uh the direction of this 144 00:07:32,466 --> 00:07:35,166 normal is seen as your circulation pass 145 00:07:35,166 --> 00:07:37,966 so that's where it is going to be positive 146 00:07:37,966 --> 00:07:39,966 and again this uh first half 147 00:07:39,966 --> 00:07:42,933 it is having this tell each divided by two 148 00:07:42,933 --> 00:07:44,933 length and second half 149 00:07:44,933 --> 00:07:49,833 it is also having this the age divider to land right 150 00:07:50,266 --> 00:07:54,200 but the path is complete and it is equal to zero 151 00:07:54,200 --> 00:07:55,866 because this circulation around 152 00:07:55,866 --> 00:07:58,666 this complete path is equal to zero 153 00:07:59,566 --> 00:08:04,700 okay now let's make the Assumption as you are 154 00:08:05,066 --> 00:08:09,366 as you are closing towards this interface 155 00:08:09,466 --> 00:08:14,100 so this means that your Bill age it is approaching zero 156 00:08:14,100 --> 00:08:16,400 so very important Assumption 157 00:08:16,400 --> 00:08:19,600 in order to determine this electric grid 158 00:08:20,700 --> 00:08:21,933 on the surface 159 00:08:21,933 --> 00:08:25,300 on the interface between these two different medium 160 00:08:26,700 --> 00:08:29,366 so once you will involve this Assumption 161 00:08:29,366 --> 00:08:32,433 that your dial age is approaching to zero 162 00:08:32,566 --> 00:08:35,066 so this time is going to be zero 163 00:08:35,066 --> 00:08:36,933 this time is going to be zero 164 00:08:36,933 --> 00:08:38,866 this time is going to be zero 165 00:08:39,533 --> 00:08:42,700 right so you are only left out with these two terms 166 00:08:43,133 --> 00:08:45,033 you simplify these two terms 167 00:08:45,200 --> 00:08:48,566 so this is the leftover term call this Del 168 00:08:48,566 --> 00:08:52,933 a Del W divide is going to cancel out in the 169 00:08:52,933 --> 00:08:54,533 in the common as a common 170 00:08:54,533 --> 00:08:56,466 and then it will be cancelled out 171 00:08:56,466 --> 00:09:01,566 on the right hand side 0 divided by that uh that W 172 00:09:01,566 --> 00:09:05,833 you know that it is equal to 0 right 173 00:09:06,533 --> 00:09:09,766 so this is the uh takeaway from these two sides 174 00:09:10,500 --> 00:09:13,933 what is this what is the intuitiveness of this thing 175 00:09:13,933 --> 00:09:14,833 this term 176 00:09:16,133 --> 00:09:17,400 the intuitiveness 177 00:09:17,466 --> 00:09:21,866 states that the tendential component of electric feed 178 00:09:22,600 --> 00:09:25,200 we are equal at the boundary 179 00:09:25,200 --> 00:09:28,300 or the interface of two different dialectics 180 00:09:29,266 --> 00:09:33,766 this means that the potential component of electrical 181 00:09:33,766 --> 00:09:37,200 undergoes no change on the boundary 182 00:09:37,766 --> 00:09:40,800 and it will stay continuous 183 00:09:41,566 --> 00:09:45,100 it will stay continuous across the boundary 184 00:09:47,766 --> 00:09:51,266 let's see what happens to the uh normal component 185 00:09:52,400 --> 00:09:56,866 so for this uh case for this case 186 00:09:58,200 --> 00:10:02,333 now let's first see for this flextance tree 187 00:10:02,333 --> 00:10:03,866 first of all flextance tree 188 00:10:04,400 --> 00:10:04,733 let's see 189 00:10:04,733 --> 00:10:07,533 what happens to this financial component of this 190 00:10:07,533 --> 00:10:08,433 flextance tree 191 00:10:08,933 --> 00:10:15,266 so since we know that uh this uh d plus 10 C 192 00:10:15,266 --> 00:10:18,066 it is equal to absent on our times electric feed 193 00:10:18,533 --> 00:10:20,900 so we involve this definition 194 00:10:20,900 --> 00:10:23,666 the constituted relationship into this uh 195 00:10:24,700 --> 00:10:26,633 first divided expression 196 00:10:26,766 --> 00:10:30,500 from here we can see that your 197 00:10:31,766 --> 00:10:34,466 d one t divided by abstinent 1 is equal to d 2 198 00:10:34,466 --> 00:10:36,700 t divided by abstinent 2 199 00:10:36,966 --> 00:10:38,900 and just simplify these two terms 200 00:10:38,900 --> 00:10:40,500 you will get this thing 201 00:10:41,700 --> 00:10:46,400 so from here you can into that potential component of d 202 00:10:46,700 --> 00:10:50,400 it is undergoing some change 203 00:10:50,566 --> 00:10:53,466 and that change across the boundary 204 00:10:53,533 --> 00:10:57,166 it is due to this dialectic 205 00:10:58,466 --> 00:11:00,300 materials are maturity 206 00:11:00,566 --> 00:11:03,666 so this means that since these two are not equal 207 00:11:03,800 --> 00:11:06,166 D1T is not equal to D2T 208 00:11:06,300 --> 00:11:10,900 so that this means that d is discontinues 209 00:11:11,333 --> 00:11:13,766 this continues across the boundary 210 00:11:13,933 --> 00:11:15,800 so remember for electric field 211 00:11:15,966 --> 00:11:18,666 dependential component of electrical 212 00:11:18,666 --> 00:11:19,933 it is continuous 213 00:11:19,933 --> 00:11:24,066 whereas the tangential component of this um 214 00:11:25,100 --> 00:11:30,466 electric flux tensity it is not continuous 215 00:11:32,300 --> 00:11:37,000 right because it is involving this permitted 216 00:11:40,133 --> 00:11:40,966 let's uh see 217 00:11:40,966 --> 00:11:45,133 what happens to the normal components of the trucks 218 00:11:45,133 --> 00:11:47,466 density and the electric field 219 00:11:47,766 --> 00:11:49,000 for this thing 220 00:11:49,133 --> 00:11:52,366 uh we will uh make sure of this Boss's law 221 00:11:52,800 --> 00:11:54,166 and as a boss can surface 222 00:11:54,166 --> 00:11:55,666 we will take this uh 223 00:11:56,400 --> 00:12:01,266 this example of a small pill box which is of 20% chair 224 00:12:02,000 --> 00:12:03,566 uh so that we can uh 225 00:12:03,566 --> 00:12:04,600 determine this uh 226 00:12:04,600 --> 00:12:06,866 normal confidential boundary condition 227 00:12:07,800 --> 00:12:10,066 so again we resolve this 228 00:12:10,066 --> 00:12:13,666 we decompose this electricity to compromise 229 00:12:13,666 --> 00:12:15,700 the financial and the confidence 230 00:12:16,200 --> 00:12:20,400 and the surface value of this wasn't surface 231 00:12:20,400 --> 00:12:24,633 it is DL s and the height of this surface it is DL H 232 00:12:25,966 --> 00:12:27,333 again the two mediums 233 00:12:27,333 --> 00:12:29,766 they are uh secreted by there 234 00:12:30,900 --> 00:12:32,700 these electric permit duties 235 00:12:32,700 --> 00:12:34,666 these are electric properties 236 00:12:36,200 --> 00:12:39,700 let's involve this possible which changes the 237 00:12:41,766 --> 00:12:43,533 the closed infigure of the dot 238 00:12:43,533 --> 00:12:46,266 d s is equal to be charged and closed 239 00:12:46,300 --> 00:12:49,666 that it reflects passing to a closed surface 240 00:12:49,666 --> 00:12:52,033 it is equal to be charged and closed 241 00:12:53,166 --> 00:12:56,300 okay so the left hand side here 242 00:12:56,300 --> 00:13:01,466 uh we are assuming that since we are approaching this 243 00:13:01,466 --> 00:13:02,266 uh 244 00:13:02,666 --> 00:13:04,366 we're approaching this interface 245 00:13:04,366 --> 00:13:07,200 so this means that this del H 246 00:13:07,200 --> 00:13:11,866 it is approaching zero so this integral for this side 247 00:13:12,266 --> 00:13:13,433 for this side 248 00:13:13,800 --> 00:13:18,666 this integral is equal to zero for this side 249 00:13:20,000 --> 00:13:27,200 and we only need to store this top and vitamin right 250 00:13:29,166 --> 00:13:30,800 yes so for the 251 00:13:30,800 --> 00:13:32,900 since it is a top product 252 00:13:33,400 --> 00:13:36,966 uh and if we see that for D 1 n 253 00:13:37,066 --> 00:13:42,966 for D 1 n the teacher of this E and the energies 254 00:13:42,966 --> 00:13:44,966 it is normal to the surface 255 00:13:45,533 --> 00:13:46,400 uh 256 00:13:46,400 --> 00:13:51,500 this E N and this e N that is the normal to the surface 257 00:13:51,500 --> 00:13:55,066 the last both are in the same direction that is your 258 00:13:56,533 --> 00:14:00,266 right the first case in the first medium 259 00:14:00,266 --> 00:14:01,566 if it is equal to zero 260 00:14:01,566 --> 00:14:05,400 so the cause of uh uh that uh zero degree 261 00:14:05,400 --> 00:14:09,733 it is equal to one and for the product specific 262 00:14:09,733 --> 00:14:11,133 they are in the opposite directions 263 00:14:11,133 --> 00:14:14,500 so that's why the angler displacement between them 264 00:14:14,500 --> 00:14:17,700 it is 1 80 degrees so that's why because of 1 265 00:14:17,700 --> 00:14:20,033 80 degree is for 2 - 1 266 00:14:20,966 --> 00:14:23,666 and uh on the right hand side 267 00:14:23,666 --> 00:14:27,833 what is in charge controls by this surface spins 268 00:14:28,666 --> 00:14:32,466 we are only on this surface here 269 00:14:33,000 --> 00:14:36,133 and let's assume that the surface identity 270 00:14:36,133 --> 00:14:38,166 on this surface it is us 271 00:14:38,600 --> 00:14:41,900 so discharged and closed by the surface 272 00:14:41,900 --> 00:14:45,066 having this surface area of dial s 273 00:14:45,066 --> 00:14:48,133 this simply is equal to the product of this war 274 00:14:48,133 --> 00:14:53,666 s times dial s so it is from your basic definition 275 00:14:54,900 --> 00:14:58,400 now this LS it is going to cancel outro 276 00:14:58,400 --> 00:15:00,366 and this is your remaining term 277 00:15:00,800 --> 00:15:03,500 so the relationship between the normal component 278 00:15:03,500 --> 00:15:05,100 of the electrical first entity 279 00:15:05,100 --> 00:15:07,933 is that the difference between the normal component 280 00:15:07,933 --> 00:15:10,533 it is equal to the social chart s 281 00:15:10,533 --> 00:15:12,566 E which is pleased 282 00:15:12,566 --> 00:15:17,533 at the interface between these two mediums right 283 00:15:17,533 --> 00:15:18,833 so this is the takeaway 284 00:15:20,533 --> 00:15:22,500 and uh uh here 285 00:15:22,500 --> 00:15:25,700 would you note that also that this is very important 286 00:15:25,700 --> 00:15:29,366 that the integration with respect to this uh 287 00:15:30,066 --> 00:15:31,066 side first date 288 00:15:31,066 --> 00:15:36,633 which is go to 0 because this time 8 which is 0 2 0 289 00:15:38,966 --> 00:15:41,166 no let's assume that this uh 290 00:15:41,166 --> 00:15:45,700 there's no charge place at the boundaries 291 00:15:46,466 --> 00:15:49,033 at the interface between these two dialects 292 00:15:49,166 --> 00:15:51,400 that is your rule as is equal to 0 293 00:15:51,600 --> 00:15:54,833 so for this case your d 1 n is equal duty to n 294 00:15:54,966 --> 00:15:58,300 this means that the normal components of t 295 00:15:58,300 --> 00:16:00,366 they are equal at the interface 296 00:16:00,766 --> 00:16:03,700 at the boundaries between these two medium 297 00:16:04,300 --> 00:16:07,400 and the normal component of electrical substance 298 00:16:07,400 --> 00:16:11,766 t undergoes more change on the boundary 299 00:16:12,000 --> 00:16:14,066 and it is continuous 300 00:16:15,500 --> 00:16:16,900 across the boundary 301 00:16:19,466 --> 00:16:21,266 now let's see what happens to the normal 302 00:16:21,266 --> 00:16:23,133 comprehend of letrophy again 303 00:16:23,133 --> 00:16:25,566 we enroll this constitute relationship 304 00:16:26,200 --> 00:16:27,566 and you can see that 305 00:16:29,000 --> 00:16:32,500 the e 1 n is not equal to 306 00:16:33,966 --> 00:16:34,933 e 2 n 307 00:16:34,933 --> 00:16:39,466 means that the electric field is this continental 308 00:16:39,466 --> 00:16:40,700 across the boundary 309 00:16:41,300 --> 00:16:43,900 so electric field normal component 310 00:16:43,900 --> 00:16:48,266 it undergoes some changes which are related 311 00:16:49,733 --> 00:16:54,466 using this electric permatuity of these two mediums to 312 00:16:54,466 --> 00:16:55,666 that is the takeaway 313 00:16:56,500 --> 00:16:58,900 right the normal component of electric fertility 314 00:16:58,900 --> 00:17:00,033 they are continuous 315 00:17:00,166 --> 00:17:03,000 if there's no surface charge density 316 00:17:03,100 --> 00:17:05,800 at the interface of these two mediums 317 00:17:07,333 --> 00:17:10,300 and uh electric uh normal components 318 00:17:10,300 --> 00:17:13,766 normal components of electricity they are this one 319 00:17:13,766 --> 00:17:15,166 yes across the bone 320 00:17:16,933 --> 00:17:17,900 select uh 321 00:17:18,166 --> 00:17:21,400 bring on these two reserves and further uh 322 00:17:21,866 --> 00:17:26,600 uh drive some of the expressions indicates 323 00:17:26,600 --> 00:17:27,700 uh if this is uh 324 00:17:27,700 --> 00:17:31,700 in face in face between these two mediums right 325 00:17:32,566 --> 00:17:36,300 and this is normal between these two mediums right 326 00:17:36,300 --> 00:17:39,633 like this thing and you can straight like this thing 327 00:17:45,900 --> 00:17:48,900 cream it is making the in the first medium 328 00:17:48,900 --> 00:17:52,133 it is making the angle of Peter 1 329 00:17:52,133 --> 00:17:55,666 like this one with respect to this one more 330 00:17:56,066 --> 00:17:59,500 and this Peter 2 for this uh 331 00:17:59,866 --> 00:18:00,666 you know 332 00:18:01,533 --> 00:18:04,300 this cheetah tool with respect to this normal 333 00:18:04,300 --> 00:18:06,766 for this electric field in this medium 2 334 00:18:07,166 --> 00:18:11,166 now let's resolve this electric field in medium 1 335 00:18:11,166 --> 00:18:13,566 on this normal like this way 336 00:18:14,400 --> 00:18:16,333 like this way right so 337 00:18:16,333 --> 00:18:18,833 you're making the projection of electric field 338 00:18:19,066 --> 00:18:23,633 on this normal on this normal direction right 339 00:18:24,466 --> 00:18:29,466 and so this normal even n it is equal to even 340 00:18:30,566 --> 00:18:33,800 it is equal to e one cause of teacher 1 341 00:18:33,800 --> 00:18:35,133 and light bulb d 1 n 342 00:18:35,133 --> 00:18:39,700 it is equal to d 1 cause of teacher 1 and e 1 t 343 00:18:39,700 --> 00:18:44,466 it is equal to e 1 sign of teacher 1 n d 1 t 344 00:18:44,466 --> 00:18:49,400 it is equal to d 1 sign of teacher one and in medium 2 345 00:18:49,666 --> 00:18:51,333 we we drop this 346 00:18:51,333 --> 00:18:55,900 we drop this comprehend on this um 347 00:18:56,333 --> 00:18:59,700 that is your normal number between these two such days 348 00:18:59,700 --> 00:19:02,666 because here we have the information of Peter 2 349 00:19:02,700 --> 00:19:05,366 which is the animal between E2 and the normal 350 00:19:05,366 --> 00:19:07,566 between these two such days 351 00:19:08,933 --> 00:19:13,600 and here we once we resolve these two components 352 00:19:13,600 --> 00:19:16,500 then we will see that E2 353 00:19:16,500 --> 00:19:23,100 it is equal to sign d tattoo and D two d 2 n 354 00:19:23,333 --> 00:19:29,666 so e 2 t it is equal to E to sign Peter 2 n d 2 n 355 00:19:29,666 --> 00:19:32,966 it is equal to d 2 cause Peter 2 back 356 00:19:32,966 --> 00:19:35,200 we're just resolving this components 357 00:19:35,266 --> 00:19:37,800 this this component on the normal 358 00:19:40,166 --> 00:19:43,200 let's make sure realization of these two uh 359 00:19:43,200 --> 00:19:46,400 things that we have drived on the previous uh slide 360 00:19:46,900 --> 00:19:52,766 uh so uh divide this equation 1 with its question 2 361 00:19:53,133 --> 00:19:54,266 use this uh 362 00:19:56,066 --> 00:19:58,966 geometric identity of the anti physical 363 00:19:58,966 --> 00:20:01,033 scientific web deposititor 364 00:20:01,733 --> 00:20:03,600 and simplify this expression 365 00:20:03,600 --> 00:20:06,000 so this is very famous uh 366 00:20:07,333 --> 00:20:13,166 uh law that is known as the law of retraction right 367 00:20:13,300 --> 00:20:17,166 and it is responsible for the bending of electric feed 368 00:20:17,366 --> 00:20:20,466 towards the normal or away from the normal 369 00:20:20,600 --> 00:20:23,400 once the dialectric property is 370 00:20:24,133 --> 00:20:27,266 are different between two services 371 00:20:28,166 --> 00:20:31,000 and here we are also having resumption 372 00:20:31,000 --> 00:20:34,633 that be interfaces free of charge 373 00:20:34,733 --> 00:20:35,666 there's no charge 374 00:20:35,666 --> 00:20:39,266 that place between the boundaries of these two mediums 375 00:20:39,466 --> 00:20:42,066 so that is only for this particular case 376 00:20:42,366 --> 00:20:45,400 this law Protection is only vertical case 377 00:20:45,466 --> 00:20:47,133 and depending upon the relative 378 00:20:47,133 --> 00:20:49,666 permativity of these two mediums 379 00:20:49,800 --> 00:20:52,500 you will see that this electric field 380 00:20:52,500 --> 00:20:55,133 it is bending towards the media 381 00:20:55,133 --> 00:20:56,400 towards the normal 382 00:20:56,666 --> 00:21:01,033 between these two mediums or away from the media 383 00:21:04,700 --> 00:21:08,133 personal discuss the second scenario 384 00:21:08,133 --> 00:21:12,933 that is your one side of the medium 385 00:21:12,933 --> 00:21:16,133 it is a dialectic and the other side of the medium 386 00:21:16,133 --> 00:21:19,200 it is a conductor perfect conductor conductor 387 00:21:19,566 --> 00:21:23,866 so this is the uh condition is the scenario 388 00:21:23,866 --> 00:21:25,533 and we have to uh 389 00:21:25,533 --> 00:21:27,900 drive the boundary conditions for the scenario that 390 00:21:27,900 --> 00:21:30,200 what happens when the electric feed 391 00:21:30,200 --> 00:21:31,766 it is going from uh 392 00:21:32,533 --> 00:21:35,666 dialectic towards the conductor medium 393 00:21:35,866 --> 00:21:37,300 so let's see what happens 394 00:21:37,400 --> 00:21:39,700 so we know that inside the conductor 395 00:21:39,900 --> 00:21:41,766 the electric field is zero 396 00:21:41,766 --> 00:21:46,433 because your conductivity of that perfect medium 397 00:21:48,666 --> 00:21:52,366 conductor it is infinity and this is um 398 00:21:52,366 --> 00:21:55,666 Shin will maintain finite condensity 399 00:21:55,866 --> 00:22:00,200 cause J Z Korro Sigma E we know that if uh 400 00:22:00,200 --> 00:22:01,900 the uh 401 00:22:01,900 --> 00:22:04,900 that you're from here you can see that is equal to 402 00:22:06,200 --> 00:22:09,733 g to have a Sigma energy Sigma is very 403 00:22:09,733 --> 00:22:11,133 very hard than anything 404 00:22:11,133 --> 00:22:14,300 to have infinity is equal to zero 405 00:22:14,300 --> 00:22:17,800 so that will say that inside the conductor 406 00:22:17,800 --> 00:22:19,666 the electric release is zero 407 00:22:21,500 --> 00:22:25,166 and we have already had the intention that uh 408 00:22:25,566 --> 00:22:28,933 the electric turn it stays at the surface of uh 409 00:22:28,933 --> 00:22:33,233 conductor and any induction of uh 410 00:22:33,600 --> 00:22:34,900 electric uh 411 00:22:34,900 --> 00:22:37,366 charge inside the inductor 412 00:22:37,366 --> 00:22:41,100 will immediately travel toward the surface of that 413 00:22:41,100 --> 00:22:43,066 conductor that's why the 414 00:22:43,600 --> 00:22:45,666 uh electric field inside the conductor 415 00:22:45,666 --> 00:22:46,833 it is equal to zero 416 00:22:47,900 --> 00:22:49,500 so now let's um 417 00:22:49,500 --> 00:22:52,366 uh solve these two things 418 00:22:52,366 --> 00:22:54,533 uh the maxifications that we have 419 00:22:54,533 --> 00:22:55,400 uh uh 420 00:22:55,400 --> 00:22:57,600 solved for the previous case as well 421 00:22:57,700 --> 00:22:58,466 so first of all 422 00:22:58,466 --> 00:23:02,800 this close line will change well around this part 423 00:23:02,800 --> 00:23:03,666 that is a B 424 00:23:03,666 --> 00:23:04,466 C d a 425 00:23:04,600 --> 00:23:07,166 the only difference in this case is 426 00:23:07,266 --> 00:23:11,466 we only have electric field in this dialect medium 427 00:23:11,766 --> 00:23:16,233 electric field in the second medium is going to be zero 428 00:23:16,900 --> 00:23:18,966 right this thing 429 00:23:19,100 --> 00:23:22,300 so the integrations with respect to this uh 430 00:23:22,733 --> 00:23:24,700 uh normal 431 00:23:24,700 --> 00:23:27,466 uh Indonesia components in the first medium 432 00:23:27,700 --> 00:23:28,766 they will stay here 433 00:23:28,766 --> 00:23:31,933 whereas the integrations in the second mediums 434 00:23:31,933 --> 00:23:33,500 they will be equal to zero 435 00:23:35,100 --> 00:23:39,133 and the just simply simplified case 436 00:23:39,133 --> 00:23:45,400 we are we are taking that e 1 t it is equal to t n 437 00:23:45,966 --> 00:23:52,200 likewise e 1 n which is equal to e n right 438 00:23:52,566 --> 00:23:54,333 because we only have the electric green 439 00:23:54,333 --> 00:23:58,766 in the plus medium that is the dialect medium 440 00:23:59,400 --> 00:24:00,500 okay now again 441 00:24:00,500 --> 00:24:01,900 involved Assumption that day 442 00:24:01,900 --> 00:24:04,266 you are approaching this interface 443 00:24:04,600 --> 00:24:08,100 so once you will approach this interface 444 00:24:08,266 --> 00:24:12,400 then this will also equal to 0 right 445 00:24:12,500 --> 00:24:14,266 and this will also equal to 0 446 00:24:14,266 --> 00:24:17,166 so what you are left with is that is this thing 447 00:24:17,766 --> 00:24:18,866 and from here you can 448 00:24:18,866 --> 00:24:24,333 into that the potential component of electric field 449 00:24:24,333 --> 00:24:27,400 it is equal to zero at the interface 450 00:24:27,400 --> 00:24:30,600 R boundaries of these two uh 451 00:24:30,600 --> 00:24:31,400 these two mediums 452 00:24:31,400 --> 00:24:34,233 that is the uh connector dielectric mediums 453 00:24:35,466 --> 00:24:39,433 and likewise your uh furniture component of your uh 454 00:24:39,533 --> 00:24:43,033 this uh electric first energy it is actually Puerto Co 455 00:24:45,766 --> 00:24:46,933 now let's see 456 00:24:46,933 --> 00:24:47,566 what happens 457 00:24:47,566 --> 00:24:50,800 to the normal component of the electric grid 458 00:24:51,000 --> 00:24:54,700 and let's see first for the electric personality 459 00:24:55,166 --> 00:24:57,466 involving involving this causes law 460 00:24:58,200 --> 00:24:59,866 and using this cause in surface 461 00:25:00,700 --> 00:25:04,166 now again in the second medium 462 00:25:04,366 --> 00:25:07,300 this electric with the zero and we are left with this 463 00:25:08,866 --> 00:25:14,400 uh DNL s is equal to the charge and closed 464 00:25:14,800 --> 00:25:16,366 and again the same Assumption 465 00:25:16,366 --> 00:25:18,533 that you're approaching this interface 466 00:25:18,533 --> 00:25:23,300 because you're Dell H it is approaching zero 467 00:25:24,300 --> 00:25:29,433 again inside this uh conductor electrical is 4:00 468 00:25:31,200 --> 00:25:34,066 and uh we know that uh 469 00:25:34,766 --> 00:25:38,366 if Ruas is placed at the interface between these two 470 00:25:38,733 --> 00:25:39,366 such days 471 00:25:39,366 --> 00:25:43,400 then the charge and close will be is equal to rosdls 472 00:25:43,566 --> 00:25:45,966 and then Ldls will be cancelled out 473 00:25:46,133 --> 00:25:47,766 and you can see that 474 00:25:48,133 --> 00:25:51,900 your normal component of lexicregency 475 00:25:51,900 --> 00:25:56,300 it is simply is equal to the surface charge density 476 00:25:56,300 --> 00:26:00,666 which is placed at the surface 477 00:26:01,300 --> 00:26:04,666 at the interface between these two mediums 478 00:26:04,666 --> 00:26:07,033 that is your conductor and the electric medium 479 00:26:07,666 --> 00:26:08,200 and likewise 480 00:26:08,200 --> 00:26:10,700 you can find out the electric feed in this case 481 00:26:10,700 --> 00:26:13,866 the normal component of the electric feed in this case 482 00:26:17,666 --> 00:26:19,866 this and aesthetic conditions 483 00:26:19,866 --> 00:26:22,000 the following conclusions can be drawn 484 00:26:22,000 --> 00:26:23,600 for a protect conductor 485 00:26:23,966 --> 00:26:29,033 that no electric feed may exist within a conductor 486 00:26:29,166 --> 00:26:31,466 because electric feed is equal to zero 487 00:26:31,466 --> 00:26:34,333 inside a connector and the volume 488 00:26:34,333 --> 00:26:36,133 charge density inside the connectors 489 00:26:36,133 --> 00:26:40,700 is also equal to zero because the electric charge 490 00:26:40,700 --> 00:26:43,700 it will immediately travel towards the surface 491 00:26:43,700 --> 00:26:47,300 of that conductor due to the high conductivity 492 00:26:48,700 --> 00:26:50,666 and if we use this relationship 493 00:26:50,900 --> 00:26:54,333 and the relationship between the potential 494 00:26:54,333 --> 00:26:55,600 and electric field 495 00:26:56,133 --> 00:26:58,333 if your electric field is equal to zero 496 00:26:58,333 --> 00:27:00,500 so the grade level is equal to zero 497 00:27:00,566 --> 00:27:04,100 so this means that there's no chain in the potential 498 00:27:04,466 --> 00:27:07,266 on the surface of this electric conductor 499 00:27:08,533 --> 00:27:11,066 and it can be said that it can be said 500 00:27:11,066 --> 00:27:15,166 that no potential difference between any two points 501 00:27:16,766 --> 00:27:18,700 inside this conductor 502 00:27:19,066 --> 00:27:21,166 and that's why we see that a conductor 503 00:27:21,166 --> 00:27:24,100 it is an equiferential body 504 00:27:25,400 --> 00:27:26,500 and the tyranese 505 00:27:26,500 --> 00:27:30,500 and electric field must be external to the conductor 506 00:27:31,266 --> 00:27:33,100 and once it is like this 507 00:27:34,366 --> 00:27:37,466 so it must be normal to each surface 508 00:27:37,666 --> 00:27:40,500 that is we don't have the 509 00:27:40,500 --> 00:27:43,600 we don't have the financial components 510 00:27:43,600 --> 00:27:47,900 inside this connector we only have the 511 00:27:48,366 --> 00:27:50,966 we only have the normal components 512 00:27:51,066 --> 00:27:53,966 we only have the electric field and that too 513 00:27:54,100 --> 00:27:58,300 it's normal component at the normal 514 00:27:58,300 --> 00:28:00,633 today this conductor 515 00:28:01,666 --> 00:28:04,700 and there is no financial component even at the 516 00:28:04,866 --> 00:28:05,566 at the 517 00:28:05,566 --> 00:28:08,866 at the surface at the interface of this conductor 518 00:28:09,533 --> 00:28:12,466 we only have the normal component of electric feed 519 00:28:12,466 --> 00:28:17,100 or electrical agency if we have the superchargency 520 00:28:18,166 --> 00:28:20,333 at the interface between these two mediums 521 00:28:20,333 --> 00:28:22,633 that is the conductor and dialectic 522 00:28:24,133 --> 00:28:27,633 and uh that is relationship between these two 523 00:28:29,500 --> 00:28:31,533 election wall and study 524 00:28:31,533 --> 00:28:35,600 this very important property of this conductor 525 00:28:35,600 --> 00:28:37,900 dialectic boundary conditions 526 00:28:38,000 --> 00:28:41,433 there is an important application of the fact that 527 00:28:42,166 --> 00:28:45,100 we know that electric field inside the conductor is 0 528 00:28:45,100 --> 00:28:50,066 so it can act as an electrostatic screen material 529 00:28:52,166 --> 00:28:57,466 so if a connector a get x 0 potential like this way 530 00:28:58,466 --> 00:29:02,100 and it is sounding a connector B 531 00:29:02,966 --> 00:29:05,433 connector B as shown in this case 532 00:29:06,766 --> 00:29:08,200 then we can say that 533 00:29:08,200 --> 00:29:12,766 B is set to be electrically screened by a 534 00:29:14,500 --> 00:29:18,266 electrically screened by a form 535 00:29:19,600 --> 00:29:24,500 other electric circuit such as conductor C 536 00:29:24,533 --> 00:29:28,966 which is outside a because this conductor a 537 00:29:28,966 --> 00:29:32,466 it will not allow any of the 538 00:29:33,000 --> 00:29:35,600 electric field to pass through it 539 00:29:36,066 --> 00:29:40,733 because the e electric field inside this conductor a 540 00:29:40,733 --> 00:29:41,966 it is equal to zero 541 00:29:43,100 --> 00:29:46,300 similarly we can see that the connector C 542 00:29:46,333 --> 00:29:49,200 outside of a is screened by a 543 00:29:49,366 --> 00:29:54,766 from this connector B 544 00:29:55,266 --> 00:29:58,233 thus here in this particular example 545 00:29:58,866 --> 00:30:01,500 this a the connector a 546 00:30:01,500 --> 00:30:03,766 it is acting as a screen 547 00:30:04,266 --> 00:30:07,700 screening or shielding material and it is uh 548 00:30:07,700 --> 00:30:11,000 very useful in your electric uh 549 00:30:11,933 --> 00:30:16,766 uh suckers that uh you can uh you can screen the uh 550 00:30:16,766 --> 00:30:17,866 it is also used 551 00:30:17,866 --> 00:30:21,033 uh to reduce the electromagnetic interferences 552 00:30:21,133 --> 00:30:24,600 interferences and the uh 553 00:30:24,600 --> 00:30:27,833 interferences due to the external electric fields 554 00:30:28,100 --> 00:30:32,833 uh on the electric secretary of your electric circuits 555 00:30:34,066 --> 00:30:36,700 so electrical conditions inside and outside 556 00:30:36,700 --> 00:30:41,266 the screen are completely independent of each other 557 00:30:41,400 --> 00:30:46,333 due to the involvement of this screening or shielding 558 00:30:46,333 --> 00:30:47,400 conductor a 559 00:30:49,766 --> 00:30:53,100 the next uh consider our third and last scenario 560 00:30:53,100 --> 00:30:55,700 that is a special case of your conductor 561 00:30:55,700 --> 00:30:59,266 dialect conditions that here for the dialect 562 00:30:59,266 --> 00:31:03,033 you are simply having the free space medium 563 00:31:03,200 --> 00:31:05,200 and we know we know that what's the 564 00:31:05,200 --> 00:31:06,800 it is a free space medium 565 00:31:06,800 --> 00:31:09,533 then it's like the relative permittivity 566 00:31:09,533 --> 00:31:11,666 it is equal to one 567 00:31:12,533 --> 00:31:15,866 and uh in this case your simply your reserves 568 00:31:15,866 --> 00:31:17,666 it will reduce to that 569 00:31:17,733 --> 00:31:20,566 your normal component of this electrical density 570 00:31:20,566 --> 00:31:22,000 it is equal to do s 571 00:31:22,400 --> 00:31:26,133 and your normal component of electric uh field 572 00:31:26,133 --> 00:31:29,633 it is equal to do s t y P epslon not 573 00:31:30,966 --> 00:31:33,900 and this financial components last 574 00:31:33,900 --> 00:31:37,000 they will stay same because it was equal to zero 575 00:31:39,466 --> 00:31:43,700 so if you must approach a conducting surface 576 00:31:43,700 --> 00:31:49,233 normally as the financial component is equal to zero 577 00:31:49,266 --> 00:31:50,366 so as some people know 578 00:31:50,366 --> 00:31:50,900 that 579 00:31:50,900 --> 00:31:54,500 we don't have the potential component in this case 580 00:31:54,500 --> 00:31:55,366 as well 581 00:31:55,700 --> 00:31:59,866 and we only have the normal components in this case 582 00:32:01,133 --> 00:32:03,866 and that is only available 583 00:32:03,866 --> 00:32:05,666 components of electric field 584 00:32:05,666 --> 00:32:07,266 and the electric first chance 585 00:32:07,600 --> 00:32:10,500 and they are related with the surface charges 586 00:32:10,500 --> 00:32:11,966 like this relationship 587 00:32:13,133 --> 00:32:18,400 so this is a complete summary of this lecture No. 18 588 00:32:18,600 --> 00:32:20,600 for different boundary conditions 589 00:32:20,600 --> 00:32:25,400 that how the normal and genitial components the vary 590 00:32:26,733 --> 00:32:29,533 at the interface between these two dialective machine 591 00:32:29,533 --> 00:32:30,633 mediums 592 00:32:31,166 --> 00:32:36,700 and if we have the information of the lactophile on 593 00:32:36,700 --> 00:32:38,200 in the in the one medium 594 00:32:38,200 --> 00:32:41,166 then we can utilize these boundary conditions 595 00:32:41,166 --> 00:32:42,766 to find all the lactophile 596 00:32:42,766 --> 00:32:46,333 and the electric first density in the other medium 597 00:32:46,333 --> 00:32:48,400 using these relationships 598 00:32:49,066 --> 00:32:51,700 and likewise it is the summary for the conductor 599 00:32:51,700 --> 00:32:53,200 dialector Bondi conditions 600 00:32:53,200 --> 00:32:56,200 and the conductor free space body conditions 601 00:32:57,600 --> 00:32:58,933 so I'm here today's lectures 602 00:32:58,933 --> 00:32:59,866 so today uh 603 00:32:59,866 --> 00:33:03,866 we study uh what is electrically bounded conditions 604 00:33:03,866 --> 00:33:07,566 what is the utilization and what are the the 605 00:33:07,566 --> 00:33:10,266 the three different scenarios uh 606 00:33:10,266 --> 00:33:13,000 for which we need to study the boundary conditions 607 00:33:13,000 --> 00:33:16,533 and which are utilized to determine the electric field 608 00:33:16,533 --> 00:33:18,166 and electric first density 609 00:33:18,333 --> 00:33:20,333 from one medium to another medium 610 00:33:20,333 --> 00:33:23,766 if we have the information of electric field 611 00:33:23,766 --> 00:33:26,233 or electric prestency in one medium 612 00:33:26,333 --> 00:33:28,600 then we can determine the electric field 613 00:33:28,900 --> 00:33:31,666 and the electric prostency in other medium 614 00:33:31,900 --> 00:33:35,566 utilizing these three boundary conditions 615 00:33:35,566 --> 00:33:36,866 that we have derived 616 00:33:38,666 --> 00:33:39,300 next time 617 00:33:39,300 --> 00:33:42,400 we will again review these electric bonded conditions 618 00:33:42,400 --> 00:33:46,900 and we will further clarify these bonded conditions 619 00:33:46,933 --> 00:33:49,600 by solving some case examples 620 00:33:49,600 --> 00:33:52,600 so this is very very important lecture 621 00:33:55,333 --> 00:33:58,166 here I thank you all if you have any questions 622 00:33:58,166 --> 00:33:59,966 uh they will be entertained uh 623 00:33:59,966 --> 00:34:03,500 to your emails or online synchronous sessions 624 00:34:03,500 --> 00:34:06,033 that we have arranged at the department