Question

A metal sphere of radius 0.37 m carries a charge 0.52 μC . Equipotential surfaces are to be drawn for 100-V intervals outside the sphere.

A)Determine the radius r of the first.

B)Determine the radius r of the tenth.

C)Determine the radius r of the 100th equipotential from the surface.

-Express your answer using two significant figures.

Answer 1

In metal sphere, Potential at the surface is given by,

V = k*q/r
V = (8.9 * 10^9 * 0.52 * 10^-6)/0.37
V = 12508 V

For 1st Equipotential Surface,
V = 12508 - 100 V = 12408 V

For 2nd Equipotential Surface,
V = 12508 - 100 *10 V = 11508 V

For 3rd Equipotential Surface,
V = 12508 - 100 * 100 V = 2508 V

(a)
Radius are as below,
For 1st Equipotential Surface,
k*q/r = 12408
(8.9*10^9 * 0.52 *10^-6)/r = 12408
r = 0.37 m

(b)
For 2nd Equipotential Surface,
k*q/r = 11508
(8.9*10^9 * 0.52 *10^-6)/r = 11508
r = 0.40 m


(c)
For 3nd Equipotential Surface,
k*q/r = 2508
(8.9*10^9 * 0.52 *10^-6)/r = 2508
r = 1.84 m