Asolid 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 =

630 V

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

In the region 0<a<b

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).

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