A metal sphere with radius 1.00 cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.40 cm. Charge + q is put on the inner sphere and charge - q on the outer spherical shell. The magnitude of q is chosen to make the potential difference between the spheres 470 V, with the inner sphere at higher potential.

Calculate q.

q = 5.84*10^-11 C

Explanation:

Given

Radius of the metal sphere, r (a) = 1 cm = 1*10^-3 m

Radius of the spherical shell, r (b) = 9.4 cm = 9.4*10^-3 m

Potential difference between the spheres, ΔV = 470 V

The potential difference of an inner sphere is given by

V (in) = kq/r (a) - kq/r (b)

while the potential difference of the outer sphere is given as

V (out) = 0

ΔV = V (in) - V (out)

ΔV = kq/r (a) - kq (b)

ΔV = kq * [1/r (a) - 1/r (b) ]

where k = 9*10^9

470 = 9*10^9 * q (1/0.001 - 1/0.0094)

470 = 9*10^9 * q * (1000 - 106.38)

470 = 9*10^9 * q * 893.62

q = 470 / (9*10^9 * 893.62)

q = 470 / 8.04*10^12

q = 5.84*10^-11 C