this is election No. 15 of M2 3 2
2 electromagnetic field period 3
today 4
we will study properties of materials and connection 5
and connection currents 6
this will cover your section 5.12 7
5.4 of textbook 8
this is academic week No. 8 of your semester 9
the learning objectives of today's lecture would be 10
to understand properties of different materials 11
so that we can study the electric field 12
propagation in that material space 13
and to understand what is convection 14
in conduction terms 15
first of all the introduction in chapter No. 4 16
the electrostatic fuse in free space over considered 17
this chapter will cover electric 18
electric fields in different types of materials 19
so materials are generally classified as conductors 20
and non conductors non 21
conducting materials 22
are usually referred as insulators 23
or dialectrics 24
so materials can be classified in terms of their 25
conductivity that is Sigma 26
and it is mailed in the Zuno SAU Mohos per meter 27
or most more commonly it is siemens per meter 28
now I will discuss properties of materials 29
and how they are classified 30
based upon this thing 31
so the most important property is conductivity 32
that is used for their classification 33
a material with high conductivity that is a Sigma 34
is very very greater than 1 is referred as metals 35
so remember this thing 36
and a material with small conductivity means very 37
very smaller than 1 38
is referred to as insulator or a dialector 39
and the materials 40
whose conductivity lies between those of metals 41
and insulators are known as semiconductors 42
the examples are at as following 43
so in the metals we know that 44
the most famous metals with higher conductivity are 45
coppernant and ammonium 46
and uh for the semiconductors 47
we know these are a silicone and germanium 48
and for the insulators or dialectics 49
the most common Artie glasson or rubber insulators 50
some conductors exhibit infinite conductivity 51
at temperatures at temperature near to absolute zero 52
so that is zero calorie and they are called 53
they are called the superconductors 54
the most common examples are aluminium 55
and let the light like 56
dielectric materials 57
have a few electrons available for productions 58
whereas the metals have abundance of free electrons 59
so that their production is higher 60
as I mention in the previous slide that the materials 61
they are classified based upon their conductivity 62
and if we start from the high conductivity materials 63
so that is the example of your conductors right 64
so in this particular case 65
the materials 66
conductivity has been layered at 20 degrees Celsius 67
temperature and at a low frequencies 68
so in that particular case under these conditions 69
these are the conductivity of silver 70
copper and gold and aluminium 71
you can see here the silver is having the highest uh 72
connectivity in this particular case 73
and then once we move down in the in between region 74
then that is your silicone and germinium 75
that is your semiconductor dialect 76
semiconductor materials 77
and once we move towards the insulators or dialectrics 78
so that you can see here the uh productivity is in the 79
it is in the range of here 80
um uh 81
uh part of 10 rays from minus 4 and micros and uh 82
PICO and uh your 83
but you can see here the different nano and nano nano 84
nano the semens per meter 85
so if we see 86
the conductivity 87
depends upon frequency and temperature 88
so these are the two things 89
so conductivity is 90
the increases with decrease in temperature 91
because of what's to decrease the temperature 92
the collision between free electrons 93
disease reviews and once you increase the temperature 94
the collision increases 95
so with the reduction of temperature 96
the conduct beauty is going to increase 97
so as we reduce the temperature up to 98
you can see that a zero gallon 99
then is that those type of conductors 100
the exhibit B superconductivity properties 101
or know if it's study 102
what is correction and conduction currents 103
and what is 104
difference between these two types of currents 105
so electric current 106
in general is caused by the motion of free electrons 107
this is the convention current 108
so current in empires 109
the two are given area is the electric charges 110
electric charges passing through that area 111
per unit time 112
so it is the rate of change of charges per unit time 113
so that is the definition we must be therefore to 114
once we talk about the current 115
so it is the rate of change of current 116
rate of change of charges 117
passing through a certain circuit area 118
so in a in a current of 1 mpair 119
charge is being transferred 120
at a rate of 1 column per second 121
so this is the your basic definition 122
so if current a Dell 123
at the differential 124
current Dell I flows to a plainer surface 125
differential surface area of a Dell s 126
then we define a technology 127
that is known as the surface current density 128
so it is the rate of this 129
this you can see that current passing through 130
current flowing through up Linar surface 131
for the differential case 132
it is the Dell I divided by that Dell s 133
so it is the number of lines 134
you can see 135
that number of lines cutting through that surface area 136
or the 137
or the current passing to a surface area of that 138
as in this case so if 139
if these two currents 140
if these two parameters that is your a J 141
the current density and your differential surface area 142
they are normal to each other 143
you know that for surface area 144
will consider the normal in this direction 145
so if the direction of normal that is your N right 146
so for example it is your L s and is your 147
and then your G it is also passing by cutting 148
cutting this surface like this one 149
then uh since it is considered as a dot product 150
so for in this particle case 151
the angle between this G and this normal to surface 152
it is it is equal to 0 degree right 153
so calls of 0 will know that it is equal to 1 154
so that's why it is the maximum current ones d er 155
once your er er this current density 156
it is making an an angle of er 0 degree 157
which is back to surface normal 158
and if the current it is not normal to the surface 159
then we involve this 160
a dot product between these two quantities 161
so if we want to find out the total current 162
finding of flowing to a certain surface 163
so what we need to do 164
we need to simply integrate this dot product over that 165
anti surface so that is your um 166
generalized definition for the current 167
for non uniform areas so 168
it is the surface integral of your dark product 169
of this condensity surface condensity 170
with respect to that differential surface area 171
what is that convection card 172
convection card does not involve conductors okay 173
and consequently does not verify the own slot 174
and occurs when the current flow flows through 175
an insulating material or insulating 176
insulating medium for example liquid gas vacuums 177
so uh the example is like so these are the medium 178
so the example is like 179
you must have seen that electron 180
electrons beam is passing through a vacuum 2 181
so this is the basic example 182
in this case no conduction is involved 183
and directly the electron beam is uh 184
uh passing through that vacuum 2 185
anti claw electron beam 186
it is bombard from the one end of the tube 187
and it is received on the second end 188
and we will see one of the example 189
one of the experiment in our lab as well 190
in which the we will project this electron beam on the 191
on some surface to see as 192
to see how it is emanating from the source 193
and how it is collecting at the destination point 194
so in this in this gate 195
you can consider like this 196
that there is a floor charge 197
floor charge of density Roe v 198
so it is a volume charge density and these 199
these 200
you can consider it is composed of these electrons 201
so if they are moving at a velocity of you 202
so if in this particular example your view 203
it is directed along y axis for this 204
this is unit access will be your a y 205
and it is only having 206
going to have the y component in this case 207
now we define now what is the differential current 208
uh in this particular case or what that case we 209
we consider for example this area right 210
this differential area in this case for this 3D uh 211
cubic ball ball 212
you can say it okay 213
so what is a dalcu 214
that you will know that it is a product of your volume 215
chart density into the differential volume 216
so as you okay 217
let me highlight like this 218
so for example it is your differential volume right 219
this is your differential volume dial B 220
this upper surface it is your dial s right 221
or any side you can see this side 222
you can better treat it like this 223
because it is cutting your direction of electron B 224
in this case than the we know from 225
from our previous match that the charge 226
it is the product of your charge density 227
multiply by that differentiate volume 228
so involve this definition further the volume 229
it is the product of your differential surface area and 230
and the third element third side 231
so in this case we have taken dial s like this one 232
the top one right 233
and this we have taken the length like this one 234
like this one okay 235
so you can take okay 236
no yes 237
you can you don't take it right 238
just take this one yes take 239
this one to take this one right 240
and take this land so that we can complete a 241
complete a volume in this case 242
and then tell us 243
is obviously cutting the direction of electronbeam in 244
which would all teach you why 245
okay then uh 246
involve the definition of your velocity 247
we know that it is the 248
it is the rate of change of your distance so it 249
so in this rate of change of speed 250
rate of change of distance 251
and if it is a in one part of your direction 252
then it is known as your velocity 253
okay so you must remember that B is equal to s by t 254
yeah B is equal to s by t 255
so in this particular example 256
the s is equal to L y 257
and the differential time is that t 258
okay so that is your velocity is your Y 259
okay not involve the definitions 260
definitions of gy gy 261
it is we know that 262
it is the ratio of the current 263
passing to that differential area 264
so it is the ratio of the life or what the s 265
and from here we plug in the value of del I 266
so plug in plug this 267
plug in value plug 268
plug in this value 269
then this Del s is going to get crossed with Del s 270
and we are only left with this one 271
so in general so in general it is only for y companies 272
so in general your G is the product of 273
for the correction grant I'm talking about 274
so G is the product of your volume chart density 275
and the velocity with which the current 276
sun moving along one particular 277
or around the 3 3 d uh 278
3 direction if it is a 3D current 279
so this is take away from this line 280
what is the conduction current 281
conduction current requires a conductor 282
so so correction conduction current 283
it is for insulator and conduction current 284
it is for conductors so conductors 285
a conductor has a large number of electrons 286
that provide conduction current 287
due to an impressed electric field 288
so once an electric field is applied 289
then the then the flow of free electrons starts right 290
so conduction current 291
has a large number of free electrons 292
No. 1 and that provides the conduction current 293
once an external electric release being applied 294
so you can take it like E 295
E right and when electric red is applied 296
we know that from our previous lectures 297
that force on a 298
on a one electron it is so F is equal to Q e 299
remember this thing the Coolens law 300
right so in this case your q is minus E 301
the electron and E is the electrocule intensity 302
so in free space 303
the electron would accelerate under the uh 304
under the influence of this external electric feed 305
in materials uh 306
in different materials 307
the electron suffers a continual collision 308
and you remember that 309
that collision is known as the Brownian motion 310
in general as well so 311
the electron will move with a different 312
rusties between collision 313
and they will collide 314
so that's why we say that once the 315
once there is a high temperature then the 316
the collision is more so 317
that's why 318
the distivity of that material is going to increase 319
let's further generalize this thing 320
the average velocity for this 321
random motion of electrons 322
under the impact of the collision 323
and under the influence of external electric field 324
is known as the drift velocity 325
the average velocity 326
so every change in the momentum of free electron 327
for example single electron E must 328
must match the applied force 329
now here we are making use of neutrons 330
two laws the 331
here it is the a physical m 332
a the second law of neutrons 333
so we know that the mass is m 334
and we know that the acceleration of your electron 335
it is the drift we lost you with respect to Tao 336
Tao we know that it is the rate of acceleration 337
it is the rate of change of year and we lost it 338
and then we create this thing using the nutrients 339
3rd law that is year 340
you think that 341
so from here you can equate this coolants law 342
force being exerted on the electrons 343
under the influence of external field 344
and then you can equate these two 345
under the impact of Newton's third law right third law 346
and this was your 2nd law 347
nutrients right 348
okay and then if you play around these things 349
so from here you can extract this thing 350
the drift velocity so here Tao is the average 351
because we're being the drift velocity 352
which is known as 353
the average velocity of the urban electron 354
under the different collisions 355
and under the backducture applied force due to a 356
due to external electric field 357
so Tao is the average time between the collision 358
m is the mass of uh electron and drift lostee 359
here you know 360
the here 361
observed that the drift 362
lostee is directly proportional to the applied field 363
that is your electric field intensity 364
now 365
if there are any number of electrons per unit volume 366
then we can define that it's volume charge density 367
it is the product of your charge 368
times number of electrons 369
so since it is a minus e charge 370
so it is minus and e the connection current is er 371
er J now Jay Z Pertudrovi 372
that is your volume volume 373
volume chart density times d drift 374
lost it so here 375
the difference here we have the 376
uh drift last year uh 377
for under the 378
under the influence of external feed and previously uh 379
in the convection current 380
this we lost was the we lost it which 381
which uh 382
with which the electron beam was bombard in the vacuum 383
two 384
now put this uh uh 385
Gypsy from here uh 386
simplify this equation so how uh uh 387
simplify this equation like this that you 388
you know that from Baum's Law 389
okay let's simplify this 390
you know uh uh 391
put this thing so let's define a technology over here 392
so this thing right 393
so this thing is known as 394
the conductivity of that material 395
the conductor right 396
we have defined this thing 397
as a conductivity of material and uh uh 398
based upon this this is the 399
this is the new version of Homslaugh that you 400
that you have seen for the uh 401
previous days you have seen BJ go to IR 402
but for this uh 403
under the impact of uh 404
electric feed and the impact of electric feed 405
and using the definition of its conductivity 406
the eh 407
we have dried another eh 408
form of orms now that is Jade equal to Sigma E 409
no a conductor has 410
we know that a conductor has abundance of charge 411
that is free to move right 412
so a perfect conductor cannot 413
contain an electrostatic field within it right 414
otherwise the presence of electric fuel inside 415
would not let charges to move freely 416
so there will be a binding 417
so next and there's consider keys 418
consider keys like this so this is your original 419
this is your original conductor right 420
it is having a 421
ample of electrons and it's having high conductivity 422
so what happens that once electric field is being uh 423
applied the external 424
this external E E is external electric field e 425
I is the internal electric field 426
so they once the electric field is applied 427
the electrons 428
they align themselves in the direction of external 429
the positive charges the positive positive 430
you can see the positive charges 431
they move in this direction 432
the negative charges they move in this direction right 433
so the natural that is like this 434
under the impact of this external feel external E 435
so first of all a lot of number of electrons 436
so electrons move in the opposite direction 437
electrons move in the uh in the direction of uh 438
your electric field and uh 439
cannot contain electroceiving 440
so otherwise the presence of E field 441
if there's a uh E field then 442
if you're not allowing free motion of the electrons 443
inside this 444
so under the impact of external electric feed 445
the positive charges move to where 446
it moves in the direction of external electric feed 447
and negative charges move in the direction 448
in the opposite direction 449
so now for this isolated conductor 450
the natural zone is here 451
there's no internal no internal lecture feel enhanced 452
no internal uh surface uh 453
volume chart density piled up inside the conductor 454
and also you can relate it in this way 455
that since the conductors 456
they are having very very high conductivity 457
so we we can see that from this forms 458
law is equal to J divide by Sigma right 459
so anything anything divided by infinity 460
infinity is equal to zero 461
so from here 462
we can also into that the electric grid inside the 463
but fact conductor is going to zero 464
and in this essential 465
will maintain a finite condensity 466
and definitely if there's a other than conductivity 467
then we will have a finite condensity 468
so in this case 469
we are going to have in finite condensity 470
okay 471
so 472
based upon the previous assumptions inside conductor 473
the es go es equal to zero 474
and so we are talking about an isolated 475
isolated a conductor and using this step in 476
the relationship between electric and the 477
electric feed and the electric potential 478
so we know that is equal to tell me right 479
so if you're is equal to zero 480
then your value is your phone going to be 0 481
so which implies that value is equal to 0 482
your potential inside that uh 483
a conductor is going to be 0 484
so this implies that value is equal to 0 485
so what happens that throughout 486
throughout the conductor 487
the potential is going to be the same 488
so it that's why we 489
we see that a conductor is an equal potential body 490
because it's difference or it's differential 491
electric potential is equal to zero 492
there's no rate of change 493
there's no change in the potential 494
over the entire surface of that conductor 495
so it is only because 496
uh because of it's uh 497
a property 498
that there's no internal electric cream inside the 499
electric inside the conductor 500
and once we involve the gauze store 501
we know that it is the close integral surface integral 502
Audi dot DS where we is equal to the volume 503
open volume to grab volume chart density 504
now in this case if your 505
this thing is equal to 0 and this thing is equal to 0 506
this this means your left hand is equal to 0 507
and it is only possible if your right hands 508
inside parameter is equal to 0 509
so for the so that thing that's why we say that roll 510
these are also equal to zero 511
so this is your takeaway from these two slides 512
that inside an isolated perfect conductor 513
your electric rate is zero 514
hence your uh this uh VAB or LB is equal to 0 515
and uh uh likewise your 516
this uh volume chart density is equal to zero 517
here we define that the AB is differential 518
difference between two points a and B in t conduct 519
now what's uh what happens 520
uh once we apply the external field 521
uh using this uh batteries right 522
and this uh 523
this potential extended potential or batteries 524
you can see that so once we apply this voltage 525
once we apply this voltage across the conductor 526
let's see what happens so 527
when a potential difference is applied 528
at the ends of conductors 529
so in that case we will have some 530
we will have some electric field inside that conductor 531
so 532
electric field is not equal to zero for the conductor 533
once the potential is being applied 534
across the conductor 535
so in this case the conductor is not isolated 536
it is a wide it is wide to a source 537
hence 538
an electric field must exist inside the conductor 539
to sustain the flow of electrons 540
the direction of electric field 541
the direction of electricity 542
so we know that under the impact of electric feed 543
uh the electro 544
and the positive charges will move in one direction 545
and negative charges will move in other direction 546
so in this particular case it is your positive 547
it is your negative 548
so electrical direction is like this 549
so your positive charges direction 550
conventionally will be also in the direction of it 551
inside electric field and your uh electrons 552
it will it will move in the opposite direction 553
so the direction of electric feed produced 554
is the same as the direction of 555
the flow of positive charges 556
or the current so conventionally what we say that 557
that it is our flow of positive charges 558
the direction of flow of positive charges 559
taken as the direction of your current 560
and uh this direction is opposite to the direction of 561
uh floor of electrons 562
and the opposition to any opposition to the floor of uh 563
this uh electrons 564
or these politic charges is known as the resistance of 565
uh uh the conductor 566
to divide the resistance 567
the magnitude of electric wheel 568
we know that 569
we have already defined that we equal to E dot DL right 570
and then we define that if this is a complete land 571
we can also needed that be equal to Ed like this thing 572
right generalize in this thing 573
we can also generalize it like this 574
so this example 575
your d is the complete land of your conductor 576
and this is your externally applied voltage 577
uh okay 578
involve this equation 579
so is equal to the ratio of from here 580
your E is equal to be upon d to this L 581
and assuming the conductor has a uniform cross section 582
that is s 583
so no involve the definition of this current density 584
that is the ratio of your current surface area 585
and also you know that J z go to Sigma e right 586
so from here you can er 587
equate equate these two things 588
so J Z go to Sigma e right 589
so from here you plug in this E 590
E inside this right 591
and then rearrange then rearrange the equation 592
such that on the left hand side 593
we have B ratio v upon I and on right side we will 594
we will we will be left with L divide by Sigma s 595
so now in while the ONSAR 596
so we know that from ONS rise we we equal to I R 597
so I is equal to V upon I 598
and from here you can introduce that your resistant 599
resistance your resistance is equal to uh 600
it is directly proportional to the length of conductor 601
and inversely proportional to the surface area of that 602
conductor and this is our main assumptions as well 603
that we are studying in our earlier classes as well 604
and this construct of integration 605
it is proportionality constant 606
in this case is 1 upon Sigma 607
and it can be defined as this row c 608
that is your resistivity in this particular case 609
so it is the reciprocal of your conductivity 610
so the cross section of the conductor 611
it is not uniform then we involve the integrations 612
integrals right 613
so for this we know that we equal to minus uh 614
integral of e dot d l and then we know that this I 615
I is equal to what was I I was equal to 616
you know 617
remember that it was equal to j dot this thing right 618
if this is not a uniform 619
then we can involve this in CHIGRE 620
that we defined on the previous life 621
so remember that uh your resistant 622
it is directly proportional 623
it increases with the length of your 624
with uh uh conductor 625
and it decreases 626
as we increase the surface of your conductor 627
uh no extra study what is part and what and what part 628
part and part 629
once your current is flowing through that uh 630
conductor and what the uh 631
floor for charges in inside that conductor 632
so first of all it depart 633
it is defined as the rid of 634
change of energy that is in your 635
in your jaws and uh 636
are also it is defined at the four times the velocity 637
so we we we're using this definition over here 638
and we involve the dark product over here from uh 639
kulinstar we know that Africa Q E 640
and that we know that is your cue 641
your cue is equal true 642
Roby where's your cube 643
that is your Roby in two 644
yeah so yeah 645
it is your volume in general or your volume 646
volume chart density right so this thing 647
like this thing you can enroll it 648
right or not rearrange this equation in this manner 649
and then we what we can define now 650
so here here you remember this definition of your G 651
so this is your G in this case 652
the current density that we define 653
so it is the product of your volume 654
your volume identity times b 655
either it is drift losty 656
or it is the motion of electron losty 657
for the case of correction 658
so here we are talking about the drift losty 659
because we are talking about the conductors here 660
okay now this is known as the jewels laws right 661
so jewels law jewels law estate 662
uh uh 663
so and we can uh 664
what we can probably simplify this is not your TV 665
TV is equal to your differential 666
volume is equal to your differential surface and 667
differential current right 668
not involve these things 669
separate these two these two things 670
separate these two things that take the length 671
differential long days 672
take the volume differential long days 673
and then involve the further definition 674
that we have already died 675
so this V is equal to the integral of e dot DL 676
and your uh uh 677
I is it nest is the surface integral of your uh 678
your density right so here you can present 679
while the top products over here right 680
like this thing the C 681
okay once we once we simplify 682
so this is the general bar equation 683
that we utilize in our physics 684
and it will further involve the arms law 685
then it can be inerated in terms of holy 686
and solely the current flowing through that conductor 687
and it is a studio resistance of that conductor 688
so it simply involve further that your vis equal to IR 689
that is your vis equal to IR 690
then it is your second definition of your FA 691
that is your vis is equal to I squared out 692
so these two equations 693
they are known as the Jules law and once said 694
we also define another technology 695
that is your PA density so 696
it is the rate of change of PA 697
with respect to your volume 698
so differential so it is your differential 699
change in the PA with respect to differential volume 700
so if we see here 701
so it is basically your intigland intigland 702
intigland inside this equation like this one right 703
so it is your e dot g 704
and then we involve g is equal to Sigma e 705
right then e dot e equal 706
we know that 707
it is the magnitude scale of that vector quantity 708
so this is your this is your PR dense t 709
which is your wrt per cubic meter 710
let's solve these examples of your book 711
so that you can further understand 712
these concepts of current density 713
and how to find out 714
the current passing to the surface areas 715
so first first of all 716
let's consider this example 5.1 717
so in this case you are given with current er density 718
the volume current density 719
you can see here the surface condensity 720
so it is a volume current density 721
because it is m pairs per cubic uh meter 722
okay and uh 723
we need to calculate the current passing through 724
a hemispherical shell it is a hemispherical 725
so that's why is theatre range it is from 0 726
2 5 by 2 for a complete vertical shell it is from 0 727
2 pi 728
that is the difference and for 5 it is it is the same 729
that is 0 0 730
2 2 pi ladies is given in these two cases only 731
the thing that we need to do is 732
we need to take the integration of this 733
this volume chart density with respect to this volume 734
current density with respect to this circus that think 735
right surface surface yeah 736
surface differential surface element 737
okay we know that train this vertical coordinate system 738
your DS 739
it is equal to rscare assigned Peter Dyd Peter er 740
and here since it is involved in body dot product 741
so only this component will see after this dot product 742
right this thing 743
now to simplify this thing 744
your R is going since both are integrations 745
they are both with this back to defiant heater 746
so R is going to come out as a constant 747
and for the first case your R is point two 748
for the second case your R is point one 749
no due to the integration in this example 750
you can see that 751
you can involve this product rule of the integration 752
or the substitution rule 753
that here we have the differentiation of sign theater 754
along with this so 755
it's integration is Science Square data divided by two 756
right or you can see that 757
you can see that you involve this barrel 758
using this substitution 759
that you have this usable to sign theatre 760
and replace this d usable to cost theatre 761
d theatre 762
and then you just integrate it and put in these values 763
and constant values of the radius 764
so this is your crime and once it is a complete square 765
then you have to simply change the values 766
limits of this data from t 2 2 767
5 and alternatively 768
the other way is from your divergence 769
theodom that is your 770
you know that it is your divergence theodom 771
right so a closing trigger log for s g dot d s 772
no y closing trigger because it is a complete volume 773
the complete sphere in this case the Smetri 774
Smetri in this case is very good 775
so for this case 776
uh you can use the divergence uh theorem 777
so 778
and that is the part of the open volume table of this 779
at the dot g 780
and if we if you take the divergence of this thing 781
divergence of this G with respect to this 782
and that low pressure in this vertical gardener system 783
you will find that that dot g is equal to zero 784
so again the current is going to be zero 785
so this is your alternative way for the closed volumes 786
remember for the closed volumes 787
let's consider an another example 788
so 789
here we are having a y with the diameter 1 millimeter 790
conducted at the given m s bars 791
and each 7 piece number of electrons per cubic meter 792
flowing and electric 793
external electric grid is 10 milliwatt per meter 794
now 795
we need to find all the chart as your free electrons 796
first of all the volume chart density 797
so that's the product of your number of electrons 798
times the uh 799
charge of your single electrons 800
so this is your volume chart density 801
okay and uh what else because here 802
you know 803
that it is your number of electrons per cubic volume 804
so this is per cubic volumes 805
that say your manager has seen this 806
uh mission at all per cubic volume 807
and then as you need to find out the current density 808
it is a Sigma times e lactropine Sigma 809
what is Sigma this is your conductivity 810
510 days for 7 and e 10 millimeterwatts like this 811
then current it is the product of G dot s and what is s 812
from here we have the diameter and radius 813
we know that it is the half of the diameter 814
so for the surface it is by our scale for this uh 815
for this uh diameter for this circular surface 816
right by your scale so you can solve this thing 817
and then uh we know that J is equal to rule v 818
uh Zhu and uh we need to find out the drift lost E 819
right and drift lost E is 820
is equal to J divided by 4 v and Jay 821
we have Drive Ruby we have drive so simply solve this 822
uh no uh 823
we have to find out uh 824
the resistance for this uh for this uh bar 825
which is having the lent of 4 metre 826
and having the cross sectional area 827
cross sectional area of 3 by 3 right 828
but in inside that there's a pole 829
there's a hole 830
hole that is running along the complete lent of 831
learning along the complete lent of like this 832
you can assume which is the complete length 833
complete dental this conductor like so 834
if you can assume it is 4 m 835
so how to find out its surface area 836
first of all 837
we have to subtract this 838
all surface area from the surface area of this square 839
so that is your uh uh 9 9 840
the 3 square 841
minus by your scale to the radius is half of your dial 842
so what is diet 843
diet is given as a 1 cm take care of these visioners 844
the radius is given in the centimeters 845
diameters and all the dimensions 846
they are given in this centimeter here in this case 847
so your surface area the surface area of the effective 848
conductive part of this ledge 849
lead material made bar it is the 9 minus five by 4 850
and then from here you can find out the resistance 851
that is the L dividers of my ass 852
no LD is before and this is your your 853
your remaining surface of your 854
that part and then simplify this thing 855
so in today's lecture we understood what are different 856
what are the properties of materials 857
and how to classify the materials 858
based upon the conductivity 859
and what ranges classify the conductors 860
dialectrics and your semiconductors and uh 861
and how they impact and uh 862
how they impact the electric grid of the conductors 863
and this we will study in upcoming uh lectures as well 864
previously 865
we started electrically inside the free space 866
then we understood 867
what is the difference between contraction 868
and conduction currents 869
and we derived it questions as well 870
followed by some examples 871
in the next class we are going to study the 872
what is the polarization in the dialectrics 873
under the impact of external electric field 874
we will understand what is the polarization 875
and determine the polarization 876
and then we will determine the dialectic constant 877
and the strength of the these dialectic materials 878
here I thank you all 879
if you have any questions uh 880
they will be entertained uh 881
through your emails or online 882
synchronous sessions 883
that we have arranged at the department