this is election No. 16 of a V232 2
electromagnetic field theory 3
today we study polarization in dielectrics 4
and dielectric core strength 5
and strength of being dielectrics 6
it should cover your 7
section 5.5 and 5.6 of your textbook 8
the learning objectives of today's electric 9
would be to understand and determine the polarization 10
dialectrics and then determine the dialect constant 11
and the strength of the dialectry 12
under the influence of external electric field 13
now first of all 14
uh again recap what is conductor and dialectry 15
the main difference between our conductor and 16
dialectry is the availability of free electrons 17
in the atomic outermost shells to conduct current 18
so for the conductor uh 19
there are more number of free electrons 20
whereas in the dialectors 21
there least number of electrons 22
in dialectry materials 23
charges are not able to move about freely 24
right and they are bound by finite forces 25
and displacement is expected only once 26
and external freely is applied right 27
so remember that in this particular case the electrons 28
they are not freely available 29
they are bounded with some forces 30
and the only way to displace them is to apply 31
external force 32
so atoms or molecules are electrically neutral 33
this we know that uh that uh uh the electrons 34
uh the electrons and uh the positive uh postrons 35
uh they will eliminate the effect of each other right 36
protons and 37
since the positive and negative 38
charges have an equal amount 39
so they will cancel out 40
so because the net charge of electrons and the protons 41
that is equal in magniture 42
so they will eliminate each other 43
now if we see 44
we consider the things that macroscopic effect then 45
so natural 46
macroscopic effect of electric field on a dialectory 47
considered an atom of a dialectric 48
as consisting of negative charges 49
that is your electron cloud 50
and for positive charges it is herbs and nucleus 51
and similarly if we consider for the molecules 52
right at the bigger 53
more bigger level a similar picture can be adopted 54
for a dialectric molecule 55
the nuclei in the molecules 56
can be treated as a positive point charges 57
whereas the electronic structure has a single cloud of 58
negative chart 59
now let's discuss what is polarization in dialectrics 60
when an external feel e is applies to what happens 61
the positive charges so this is the state 62
once there's no external electric feel applied 63
and this is the case 64
once external feel is being applied 65
support posture 66
charges are displaced from its ecliprian position 67
in the direction of external electric field right 68
the positive charges will move in the same direction 69
that is the direction of your electric field 70
and negative charges 71
they will move in the opposite direction 72
this will discuss in our previous lecture as well 73
so 74
the force being exerted by the external electric field 75
it is for the posture charges 76
it is Q e right 77
and similarly for the negative charges 78
it is in the opposite direction 79
so it is again the Q e 80
and since Q is in magnitude it is same in both 81
in both cases so a Dipo 82
so what happens 83
that a Dipo reserves from the displacement of charges 84
and the dialectic is set to be polarized 85
so under the impact of external electrified 86
the uh the dialectrics is set to be polarized 87
and how does this dipole uh 88
dipole is the coming into K or coming into build up 89
that your positive charges are going over here 90
your negative charges are piling over here 91
and it will see in this figure in polar state 92
the electron cloud is distorted by the external E field 93
the distorted charge distribution is equaled by 94
principal of superposition 95
so you can consider like this way 96
that it is your original 97
it is your original charge distribution inside the uh 98
inside the uh this uh 99
whatever molecule or electron or dielectric 100
which is having a distribution of electron 101
atoms and molecules and plus 102
a dipole is building up areas where deposit charges 103
going on the right hand side 104
in the direction of your external e feel 105
and possible charge charges building up on the 106
it's left hand side here so 107
so you can see that in the poor eyes straight 108
that the distorted charge distribution is equivalent 109
by the principle of superposition 110
to the original charge distribution 111
that is your 112
without the influence of external electrical 113
plus a dipal movement which has created 114
due to the deformation of molecules 115
under the impact of your external electrical 116
so that 117
they are forming upper upon a typal moment over here 118
now if we see this thing 119
in terms of mathematical formulation 120
so a typal typal moment is created 121
so in this case this the distance 122
the smaller distance 123
between the negative and positive charge 124
accumulation of this typole 125
and if there are a number of typoles are building up 126
then we know that 127
it is simply a superposition of each of the typoles 128
that we cater them in the form of mission 129
and as a major of intensity of polarization 130
now let's define a term polarization 131
so the polarization it is defined as the typo moment 132
typo moment per unit volume 133
so the total typo 134
so the total diaper moment per unit volume right 135
so it is in the coolums per meter scale right 136
so as you can see here that it is coolum in 2 meter 137
and it is meter cube right 138
so after translation it is coolum per meter scale 139
there are generally two groups of uh dialectrics 140
the first one is the non polar 141
and the second one is the polar 142
so non polar dialectric molecules don't possess diples 143
they don't possess diples 144
until we apply an external electric fee 145
so major effect of extra electric field on a dialectry 146
is the creation of the type of moments 147
that align themselves in the direction of external 148
electrically 149
that we discussed in the previous site as well 150
so the examples of non prototypes of dielectrics are 151
hydrogen oxygen 152
nitrogen and rare gases that is your neon 153
your krypron your argan your xenon yeah 154
you can study on the internet as well uh 155
and then what is polar polydylectrics 156
so in the polydylectrics 157
molecules have built in permanent dipoles 158
so they already have the typos between 159
in them by default 160
and that they are randomly orientated 161
so in this case you can see 162
they are randomly oriented in different direction 163
and once we apply the external electric fee 164
the typo movements are get 165
get themselves aligned 166
in the direction of external electric fee 167
so polarization of porno molecules 168
so it is in the in the first direction 169
it is in the first figure a 170
it's a permanent iPod 171
without an external electric field 172
and it is getting its set line in the directional 173
external electric field 174
once we apply the external electric field 175
so the examples are your water 176
your sulfur dioxide and hydrochloricasia 177
so when uh when polarization occurs 178
two charge identities are forming up 179
so what are those two first one is if on its surface 180
and the second one is inside its warning surface 181
and warning so an equivalent surface chart density 182
raw PS is formed over the surface of the dialectry 183
and where in this particular 184
in the particular case we relate this thing at the top 185
product with the normal office surface 186
and it is 187
is polarization so that we discuss what it is 188
it is the sum of the diable moment per unit volume 189
okay and what is forming up inside its volume 190
that is related with rope BB 191
and it is the divergence of 192
it is related as the minus divergence of its orization 193
uh uh 194
in this uh 195
case there is a differentiation between the uh 196
this circus 197
and volume chart densities that we discussed earlier 198
so they were free they were free chart densities 199
we are whereas in this case 200
we are having bound 201
are surface and volume chart densities 202
because they have been created 203
under the influence of external electrical 204
because the uh dialectric has been polarised 205
in this case 206
no bond 207
charges 208
are those that are not free to move within the dialect 209
material and they are caused by the displacement 210
that occurs on the molecules 211
scale during polarization 212
so bonding is always related under 213
due to the external electric field 214
and free charges are those that are capable of moving 215
or microscopic distances for example 216
the electrons in a conductor 217
and the other stuff that we control 218
once we apply the external voltages 219
or the external fields 220
so this is the difference between these two things 221
if the entire dialectric were electrically neutral yes 222
we know uh 223
and prior to the application of electric field 224
and if we are we have not added an additional field 225
additional charge Ruby inside that dialectic 226
we haven't added an additional charge inside it 227
then the dialect will remain electrical neutral 228
uh even if we apply the uh external electric fuel so uh 229
if we if 230
uh electric fuel 231
if a dialectric is electrically neutral 232
prior to the electric wheel 233
and if we haven't added an additional charge into it 234
then it will stay electrical neutral 235
even if we apply the external field 236
that is we 237
it is coming into the polarization state 238
the tutorial charge of the dialectic remains zero 239
because of its neutrality 240
and uh 241
here we can see that uh 242
there again due to this thing 243
the surface charges and the warning charges 244
they will be equal in magnitude 245
but they will be opposite in uh 246
in the quality 247
so that they can cancel out each other's impact 248
uh if we consider for the surface charges 249
uh for the surface charges again 250
it is uh 251
for under the bound condition 252
the total bound surface charges 253
it is the uh 254
surface integral of your bounded uh 255
uh surface 256
uh identity 257
and uh 258
we know we 259
we we know by the definition it is p dot e n 260
since it is a surface differentiality right 261
you can write in the dark notation as well in this case 262
and in the second case uh 263
your uh volume 264
bounded volume it is uh charges 265
they are uh 266
equal to equal in magnitude 267
but in the opposite direction to the 268
that your surface chargers 269
now in this case uh 270
first of all you find this thing again 271
by taking the volume trigger of this uh 272
uh bounded volume 273
uh chargers t and from the equation 274
you know that it is minus dimensions of polarization 275
put this thing back into this equation 276
and if you see there that these two things 277
these two things are also equal to each other 278
due to this divergence theorem 279
if you remember this thing right 280
divergence theorem 281
so they will also cancel out the industry as well 282
and they will also cancel out industry as well 283
that the next charge for this dialectric 284
under the influence of external electrical 285
will still equal to zero 286
so that's why they will cancel out each other and that 287
and that and the 288
even under the polarization 289
this will be 290
this dialect will stay electrically neutral 291
or if the 292
if the dialectric region contains a free charge 293
with a volume density of raw v right 294
so the total volume charge density is the 295
so now in this case 296
there's an additional free charge density inside the 297
inside the dialectly that is your Ruby 298
which is your conventional chartency 299
and no this is your chartency 300
under the entrance of polarization 301
so the overall chartency 302
the overall total while in charge ency will be this 303
some of these two 304
now if we apply the Maxwell's first equation 305
that is the divergence of your electric 306
first density is equal to your 307
this volume chart density 308
uh then in this case you 309
you know that d is equal to Abslineaut E 310
and put that in uh 311
Absline will come over here and uh 312
put this uh 313
route is equal to this mission of these tools 314
volume chart and stays and then from here you can uh 315
play around with equations 316
you can uh 317
yeah 318
you can put this raw PV is equal to minus that dot b 319
and then you rearrange this equation from here 320
you take out this Ruby and then uh 321
you can see that uh in this case is your density 322
if you uh you have this analogy of this uh 323
this like 324
like this was your max or specification right 325
if you have the analogy of these two things 326
and you take out this rule in this case 327
so in this case your d will be equal to this 328
some of this astronaut E+ B 329
so this means your 330
your electric feel is going to increase 331
inside the dialectric 332
right inside the polarized dialectric 333
so let's related to in terms of your definitions 334
that 335
application of external electric feel causes deflux 336
density to be increased 337
as it was uh without diploradation 338
so without diploradation it was this one right 339
so 340
once it is coming under the influence of polarization 341
under the influence of an external electric feel 342
so what is going to happen 343
the neck effect of dialectry on the electric feel 344
is to increase d inside it by an amount of p 345
and that p we have already defined what is that p 346
so for the dialectry so 347
the application of electric V to dialecting materials 348
causes that is the under the polarization 349
the electric field inside the dialect 350
it is going to increase right 351
uh causes the flux 352
energy to be greater than it would be 353
in the free space right 354
once there will be no external electrical 355
so remember that thing 356
under the impact of external electrical 357
the uh 358
the neck electric field in uh 359
inside the dialectic is going to the 360
going to be increased by amount of P 361
so polarization electrifying another term 362
polarization 363
is proportional to the applied electric field 364
that is like this thing 365
and these two are the constant of uh uh 366
proportionalities and here this 367
uh uh this 368
uh 369
Kai Kai you can say it 370
Kai or shy will say it 371
is genoted as 372
the electric susceptibility of the material 373
and susceptibility of material 374
describes how quickly it responses 375
or how immediately or how um 376
effectively it responses to an external electric Bill 377
and it is contributing towards its polarization shape 378
so the higher this susceptibility often material 379
the high will be its forization 380
and high will be its internal increase 381
in the dialectric 382
in this electric grid density 383
no betting on uh 384
previous slide uh televisions 385
uh we were to find that the uh overall 386
uh dialectric 387
uh 388
this electric frequency 389
is going to increase by the amount of polarization 390
and if we involve the definition of this polarization 391
we can rearrange this equation 392
and then we can define further things that here 393
right here this 1+ Chi 394
1+ K is equal to your relative permittivity right 395
relative parametivity 396
remember it is relative permittivity 397
and it is also defined as the ratio of your uh 398
permittivity of dialect with uh 399
with respect to the parametivity of uh free space 400
that is your tenders from minus uh 9 / 36 pi r 401
8.852 into tenders 12 minus twelve feathers 402
uh by major so uh the overall 403
the overall uh uh that uh dialectric uh dialectric uh 404
so overall electrical density it is uh in a 405
in a July form it is equal to uh ABS not E 406
and if it is as free space then is epslon R 407
it is going to be one 408
then it is the same thing that is your epslon r E 409
so if the electric field it is in the presence of your 410
if it is passing to a dialectry 411
then it will be increased by an amount of this 412
amount of this uh your polarization factor 413
and uh further your uh abstinent 414
it is either it can be defined as a ratio of abstinent 415
abstinent art 416
abstinent art that I do permitting and uh an R 417
it can be defined in terms of the uh 418
this uh susceptibility 419
electronic electric susceptibility 420
uh that is the uh 1+ X E so that has two uh two things 421
uh two equations for this uh absline R 422
so the dialectic constrain or relative permitivity 423
so remember so we also name this epsilon R 424
as the dialectic constrain 425
is the ratio of permittivity of dialectic to dialect 426
free space 427
here Epstein are 428
and the sky are dimensionless because they are ratios 429
and what else 430
whereas Epstein and Epstein not 431
we are in Paris by metre 432
and a dialectic constant 433
values may change with frequency 434
so they are functional for frequency 435
we will study this thing in our common lectures 436
how they are dependent upon the frequency 437
and absline r is greater than 438
Epstein R is always greater than r equal to Trinity 439
so once it is a free space then Epstein R is equal to 1 440
and for 441
and for free space and non dialectic materials 442
that is your matters your conductors 443
it is one and for dialectic materials it is 444
it can be greater than one 445
what is 446
when the electric feel in a 447
in a dialect is sufficiently large 448
so once we apply an external electric feel 449
sufficiently large and then what happens it 450
it it starts to pulling out 451
electrons out of their molecules 452
and the dialectic becomes conducting no 453
so the electrons they know 454
they are no more stays 455
bounded under this phenomena of dialectic breakdown 456
so it is it is converting into a 457
it is converting into a conductor 458
like things that the electrons 459
they are not freely available no 460
once the externally applied electric release 461
sufficiently high so that 462
it can pull out the electrons from extra molecules 463
and they start moving freely inside the dialectic 464
so this phenomenon is known as the dialectic plate on 465
and uh it depends on the nature of the material 466
uh the temperature 467
the uh means the environmental condition 468
the temperature humidity 469
and the amount of time that we apply the electric fee 470
and what is the dialector strength 471
it's the minimum value 472
it's the minimum value of electric cream 473
at which electric breakdown occurs 474
that is known as the dialect strand 475
of the dialect material or it is 476
the dialect strand 477
is the maximum electric field that are dialectic 478
and target or grid stand without the breakdown 479
till the time the breakdown has not occurred 480
so remember 481
our dielectric is never an IDL diel so it can 482
it can be converted into a conducting die materials 483
once we apply the sufficiently large external 484
electrically 485
well 486
let's solve a couple of examples so that it makes you 487
this topic more clarified 488
so a dialectric Q of site L 489
it is centered at the origin and uh 490
the polarization of H C it is the a r right 491
it is a constant r r is 492
we know that it is a position vector 493
so find all the bound charges 494
and show that the total bound charges vanishes 495
let's see here that so is constant over here 496
remember is constantized your position factor 497
so for each side so first of all 498
always remember 499
you have to plot these things like this right 500
it is oriented along this 501
this is your cube like this one right 502
so let's take the this is your X for example 503
right and this is your first phase 504
so you normalize a X in this case right 505
and that's that's five 506
that's there are five other phases as well 507
so total six phases first of all 508
determine the bounded surface charge 509
on this first phase different phase you can see 510
so here since it is centered 511
centered on the origin 512
so the front side it will be at the distance of Albi 2 513
right and the rear 514
and the rear one will be at the distance of uh 515
by 2 as well right 516
and likewise is right hand side 517
its right hand side 518
it will be at the distance of Albi 2 519
and its left hand side 520
will be also at the distance of Albi 2 521
okay now let's find out your surface and c 522
so it is 523
we know that it is b dot e n and for this front side 524
this E n is x n uh 525
for that we also know that this side for this thing 526
it is x is equal to uh add by two constant 527
uh no 528
uh the chart product right 529
and then we have to evaluate this exit L y 2 530
so this is your set boundary surface chart identity 531
uh now the 532
we educate this thing 533
so that we can find out the total surface chart 534
because we have to find out the total charge right 535
so that with 536
that is equal to the surplus integral of this 537
bond with surplus identity 538
for this surface for the current surface 539
we know that it is varying with respect to its y and Z 540
and because the X is constant in this case 541
that is your L by 2 and the ranges 542
they are varying from minus L by 2 to L by 2 543
this thing and 6 we are consuming the 6 544
6 faces so we multiply the charge of 1 545
1 surface with 6 so 546
in order to find a big total charge on all six faces 547
okay so this is uh Royce 548
Royce Uhropious it is here by 2 549
it is coming out as a phone stand and this is the ear 550
the digital disintegration so it is the area 551
it is the area of one face that is your L square 552
L into L L square 553
so this is your 3 a L Q 554
let's find out the volume chart text 555
it is your minus 10 dot b and you measure P 556
it is in the R you take the dot product of this 557
so it is simply as it is simply you can take like this 558
that the take the divergence 559
take the divergence 560
so it will be a sum of x plus y plus Z 561
and we know that X is equal to 562
X is draining from your constant 563
so once you take the divergence 564
with the delevative of x with respect to x is one 565
delegative of y 566
respect to y is 1 and then it is 1 + 1 + 1 567
and then is constant in that 1 + 1 + 1 568
right and is constant 569
so it is coming out to be minus 3 8 570
indicate this over anti volume 571
for the volume of a q 572
we know that it is at q if it is equal dimensional 573
and some of these two charges 574
total charges 575
you can appreciate this thing that under polarization 576
this dialectric is still electrically neutralized 577
let's solve another example 578
the electric intensity in a Polish screen 579
uh is this one 580
the relative permittivity is given and uh 581
palaterate capacitor is having the uh 582
voltage applied across this 583
it is 10 kilowatt per metres 584
per metre for the electric intensity is given as a 585
10 kilowatt per metre if you 586
and the distance between that plate is 1.5 millimeters 587
so always take care of these units 588
now 589
we need to find out the DP and the surface and bomb 590
charterance trees and things like this 591
so let's solve them one by one 592
so we know that the d the fluxency 593
it is equal to your absline e 594
Absline is absline r Absline r 595
simply solve this equation e 596
it is 10 kilo watt per meter 597
so this is your 598
uh this platter prostitute 599
uh under the polarization state 600
for this dialect and what is polarization 601
polarization it is your Chi epslon r e e e and the sky 602
it is equal to epslon r minus 1 603
so all the equation to get its answer 604
then your P destroys your free 605
and the question is your free charge 606
your free charge is d dot E N remember it is d dot E N 607
and this rope bounded you're bounded 608
uh bounded surface chart and see it is peed audio right 609
so you can uh you can find it out that it is basically 610
it's magnitude it's magnitude uh 611
because this is also a normal direction 612
it is also normal direction 613
so overall it would be the magnitude of the end 614
and also it will be the magnitude of this P m 615
the second case 616
and how to find out the potential between players 617
this will know that it is called what you need to 618
d is given is given 619
so this is your answer for this game 620
let's follow another example 621
a dialectic sphere of radius 10 cm 622
has a point charge of this 623
centered at it is origin 624
and uh what we need to calculate the surface 625
dance to your polarization charge 626
on the sphere of uh 627
on the surface of square 628
before suggested by the charge honour 629
uh 630
minus will be cocoon point placed on the sphere of uh 631
surface of the sphere 632
learn a solid Azuma point charge is a located region 633
and the standard equation from 634
coming out from the cooling star is 635
Judy Webber for by apslon or scale 636
no hair 637
see that the apslon is replaced by absolutely not 638
we are because here we have the dialect sphere 639
it's not a free space media 640
and the second thing 641
we need to find out the polarization 642
right and okay 643
so the polarization we know that it is a Chi epslon r E 644
simply replace this your hair like 645
like this one and then epslon R will be cancelled out 646
so this thing 647
you have to solve to find out this surface 648
charge identity under the impact of orization 649
because it is a p dot a n 650
and here a n is equal to a r 651
because things are eminating in the radial direction 652
for this radical coordinate system 653
now take the dot order so a dot will be cancer 654
it will be dotted is equal to 1 655
and only your left your left to solve this equation 656
right solve this thing to get this answer 657
what is force the force between 658
so force again force again 659
if I utilize this columns 660
law 661
and hold only the differences that you have to replace 662
this action repeat 663
Abslan r Abslan R 664
the last example 665
find the force with which the players of a parablade 666
capacitor attract each other 667
and determine the pressure on the surface of the plate 668
due to defeat solution 669
uh from the previous lectures 670
we know that the electric field 671
intensity on the surface of each page is uh 672
R 0 s divided to action E 673
and right so it is your uh 674
electric field between uh the two panel plates 675
okay and where in is the normal to the plate 676
and so this is the electric 677
we testing on the surface of one plate right 678
uh and rice is the surface identity 679
and we have to find out the force 680
so that we can find out the pressure uh 681
so the force is tuned to E to plug in this E 682
your hair right 683
your hair and Q 684
Q will know that you will know that it is 685
it is D surface chart 686
and C times the area of that surface 687
so it is the basic definition 688
plug in this thing below the SS will be 689
coming in the numerator right 690
and then what you can play it on 691
you can play it on so it is simply fine uh 692
rosecare to epstonaut so epstonaut here 693
as you have to use epstonaut 694
epstonaut you have to replace with epstonaut e 695
r because it is a dialect 696
k and in case of a dialectic and 697
then how you can simplify it further 698
so you force no 699
you want you want to find out the force 700
your force is equal to Q E 701
right so this is coming out from here 702
right right here 703
and then you can simplify like this thing 704
that you can also write the thing 705
this role as in terms of your Q as well 706
so involve the definition of Q 707
so the expression will be in terms of your Q 708
so either you write in terms of the charge 709
or the service chart density 710
it is the same thing 711
no pressure so pressure is enforced first unit area 712
right so this area is going to cancel now 713
and you will be left out with this pressure term 714
assignment for your this lecture week No. 8 715
that is your job to solve these three exam 716
the three problem exercises 717
from your second edition of textbook 718
and you have to submit after the 719
at the beginning of the next week 720
after the interactive section for session for this 721
to lectures 722
some new previous lectures 723
so so first of all 724
we understood what is polarization in the dialectrics 725
then 726
how to determine the polarization in the dialectries 727
and the influence of external lactropine 728
then we uh we studied what is the dialectic question 729
and how to determine the 730
and what is this dialectic strength 731
and how to determine the dialectic question 732
of a dialectric 733
in the next class 734
we will study some more types of the dialectrics 735
these are the linear 736
isotropic and homogeneous dialectics 737
we will study what is the continuary equation 738
and how to determine the relaxation time 739
for the dialectrics 740
here I thank you all if you have any questions 741
uh they will be entertained 742
uh with your emails or online 743
synchronous sessions that we have arranged 744
at the department