1. (4 pts. each) Consider two concentric conducting spherical shells. Inner shel

Question

1. (4 pts. each) Consider two concentric conducting spherical shells. Inner shell carries an excess charge of +2 C and outer shell carries +4 0. In the figure, the inner shell has an inner radius of a and an outer radius of b, and the outer shell has an inner radius of e and an outer radius of d. What are the excess charges on the four surfaces? (1.1) Inner surface of small shell at r-a from the center: ( 1.2) Outer surface ofsmall shell at r-b from the center: (1.3) Inner surface of large shell at rec from the center:( (1.4) Outer surface of large shell at rd from the center: A spherical Gaussian surface is constructed at b

Explanation / Answer

1)

The charge on the inner surface of the inner shell (r = a) = 0

2)

Given that the inner shell has an excess charge of 2 uC . Therefore the charge on the outer surface of the inner

shell (r = b) is 2 uC

3)

The charge on the outer surface of the inner shell will induce an opposite charge of equal magnitude on the inner

surface of the outer shell. Hence the charge at r = c is -2 uC

4)

The charge on the inner surface of the outer shell will induce an opposite charge f equal magnitude on the outer

surface of the outer shell. The induced charge is 2 uC The outer shell already carries 4 uC. Hence the total

charge on the outer surface of the outer shell (r = d) is = 2 uC + 4 uC = 6 uC

5)

The total charge enclosed inside the spherical gaussian surface outside the shells is the sum of excess charges on

the inner shell and the outer shell. Hence the charge at r3 is 2 uC + 4 uC = 6 uC

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