A solid metal sphere of radius a = 2.5 cm has a net charge Qin = - 3 nC (1 nC = 10-9C). The sphere is surrounded by a concentric conducting spherical shell of inner radius b = 6 cm and outer radius c = 9 cm. The shell has a net charge Qout = + 2 nC. What is V0, the electric potential at the center of the metal sphere, given the potential at infinity is zero? V0 =

Question

Physics

Bronson Cunningham

31 January, 00:32

A solid metal sphere of radius a = 2.5 cm has a net charge Qin = - 3 nC (1 nC = 10-9C). The sphere is surrounded by a concentric conducting spherical shell of inner radius b = 6 cm and outer radius c = 9 cm. The shell has a net charge Qout = + 2 nC. What is V0, the electric potential at the center of the metal sphere, given the potential at infinity is zero? V0 =

+3

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Aaron Campos · Answer 1

Answer: 630 V

Explanation: In order to solve this problem we have to consider the potential given by:

In the region 0
V (r) = - ∫E*dr where E can be calculated by Gaussian law then E = k*qa/r^2

where qa=-3 nC

then

The V (r) = k*qa/r+C C is zero since V (r=∞) = 0

Finally we have

V (r) = k*qa (1/r) - (1/b)

thus V (a) = k*qa (1/a) - (1/b)

Replacing the values V (a) = 630 V, as the solid metal sphere is a equipotential object thus at the center have the same value of V that in r=a (630 V).