Question

A metal sphere with radius ra = 1.30cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.90cm . 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 480V , with the inner sphere at higher potential.
Part A

Calculate q.
q =................C

Answer 1

Answer:

$7.9902734304\times 10^{-10}\ C$

Explanation:

k = Coulomb constant = $8.99\times 10^{9}\ Nm^2/C^2$

$r_1$ = 1.3 cm

$r_2$ = 9.9 cm

V = Voltage = 480 V

Potential difference is given by

$V=kq(\dfrac{1}{r_1}-\dfrac{1}{r_2})\\\Rightarrow q=\dfrac{V}{k(\dfrac{1}{r_1}-\dfrac{1}{r_2})}\\\Rightarrow q=\dfrac{480}{8.99\times 10^{9}\times(\dfrac{1}{0.013}-\dfrac{1}{0.099})}\\\Rightarrow q=7.9902734304\times 10^{-10}\ C$

The charge is $7.9902734304\times 10^{-10}\ C$