00:01
Hello students, in this question we are given that an arrangement of concerted conduction spherical cell will kept here and a charged particle is kept at the center of the concentric cells.
00:13
We are given the graph of the flux varying with the radius or the radius, which is the distance from the center.
00:24
We are given the graph or the flux versus distance from the center.
00:29
And now, first of all, we are given this value of psi s, the magnitude of psi s as 6 .0 times 10 to the power 5 newton per meter square.
00:39
And the first part of the question, we have to calculate the magnitude of the charge particle which is kept at sit as at the center.
00:49
So, first of all, let us assume that the charge particle has a charge of magnitude q, subscript, p.
00:55
Now, we can say that according to gauss law, that through any gaussian surface, the net flux through the gaussian surface is equal to the charge enclosed within the gaussian surface divided by epsilon not, where epsilon not is the permittivity of free space, where this epsilon not is permittivity of free space, where this epsilon not is permittivity.
01:30
Permittivity of free space of free space which is also equal to whose magnitude is equal to 8 .85 times 10 to the power minus 12 ferrat per meter which is equal to ferrat 8 .85 times 10 to the power minus 12 ferrat per meter.
01:56
Ferret per meter so first of all let us assume a gaussian surface in this contracting surface this region one is assuming our gaussian surface 1 and upon its gaussian surface we apply this gauss theorem which would be equal to the net flux in this gaussian surface in surface 1 the flux would be equal to flux which would be given in the graph given as minus of 1 .8.
02:37
This region is, this point is minus of 1 .8 times 5 s.
02:47
So the net flux in this gaussian surface is given as minus of 1 .8 times minus of 5 s times to the net charge enclosed, charge enclosed divided by the epsilon not and upon cross multiplying the charge enclosed would be equal to permutivity of spree phase times minus of 5 s times 1 .8 upon substituting the values of epsilon not that is equal to 8 .85 times 10 to the power minus 12 times minus of 5 s 5 s value is given to us in the portion as 6 .0 times 10 to the power 5 times 1 .8 and upon calculating this value a charge of particle charge would be the net charge of the particle kept at the center that would be equal to coming out as minus of 9 .55 times 10 to the power minus 6 column so this is the net charge of the particle capped at the center.
03:59
Now, in the second part of the question, we are being asked to calculate the net charge on the shell a.
04:07
So, again applying gauss theorem, again applying gauss theorem, first we have to assume the gaussian surface that we are going to combine.
04:19
So let us take the gaussian surface in between this region.
04:22
This is a gaussian surface 2 which is a complete sparing spare.
04:29
So the net charge in this gaussian surface, first of all the flux for this gaussian surface is given to us as in this graph is given to us as 0 .8 times 5s.
04:41
So as we can i see that the net flux according to this graph for the region between a and b, concept of sparrar is given as 0 .8 times of 5s.
04:51
So the flux is known to us and we have to calculate the charge on surface b.
04:57
So we can write this as according to gauss surface, according to gaussian law, the flux through surface 2 would be equal to the charge enclosed.
05:08
Again, the charge enclosed in the surface 2 divided by the epsilon 0, we can calculate the charge enclosed in option of surface 2 that would be equal to the flux of the surface 2 that we calculated as...