Two hollow conducting spheres have a common center O . The dimensions of the sph
ID: 2134469 • Letter: T
Question
Two hollow conducting spheres have a common center O. The dimensions of the spheres are as shown. A charge of -100 nC is placed on the inner conductor and a charge of +70 nC is placed on the outer conductor. The inner and outer surfaces of the spheres are respectively denoted by A, B, C, and D, as shown. In Fig. 22.3, the radial component of the electric field, at a point that is 0.40 m from O, is closest to:
Two hollow conducting spheres have a common center O. The dimensions of the spheres are as shown. A charge of -100 nC is placed on the inner conductor and a charge of +70 nC is placed on the outer conductor. The inner and outer surfaces of the spheres are respectively denoted by A, B, C, and D, as shown. In Fig. 22.3, the radial component of the electric field, at a point that is 0.40 m from O, is closest to:Explanation / Answer
The main thing to keep in mind here is that the electric field inside of a conductor is zero. So, if you take a gaussian surface inside of the conductor, there needs to be no net charge, ie the amount of positive charge inside must equal the amount of negative charge so the total charge is zero.
The first thing this implies is that there cannot be any charge on surface A, because there would be no positive charge to cancel out the negative charge. So, all of the charge on the inner conductor has to be spread out over surface B.
Now, looking into the second conductor, the charge enclosed in a gaussian surface through it has to be zero. So, if there is -200 nC charge on the surface B, there has to be +200 nC charge on the surface C. Since there is only +80 nC excess charge on the outer conductor, you end with a negative charge, 200 - 80 = 160 nC. So, all this charge goes to outer surface of the larger conductor, surface D. So,
A has no charge
B has a -200 nC charge
C has a +200 nC charge
D has a -160 nC charge
A good way to confirm this is to take a gaussian surface outside of both conductors. The net charge enclosed is -200 nC + 80 nC = -120 nC. So, this looks like a single sphere with -160 nC charge on its surface.
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