A non-conducting sphere of radius R = 5 cm has its center at the origin O of the coordinates system as shown in the figure. It has two spherical cavities of radius r = 1 cm, whose centers are at (0, 3 cm), (0, - 3 cm), respectively, and the solid material of the sphere has a uniform positive charge density .Compute electric potential at point P (4 cm, 0)

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 2)

Answer 1

Concept

The electric potential inside a uniformly charged sphere is,

Where

R = radius of the sphere, r is the distance from the center of the sphere (r < R)

Electric potential outside a uniformly charged sphere is, when ( r > R)

Calculation:
Given: Radius of sphere R = 5 cm = 0.05 m

The radius of the cavity r = 0.01m

Charged density ρ = 1/π μ C-m^-3

Calculating the charge on the sphere

=

Q = 1.667×10^-10C

Charge in the cavity q

= 1.333 ×10^-12C

The electric potential at point P (4 cm, 0),

Hence the electric potential inside the charged sphere at the point P is 34.92

Additional Information

Derivation of the electric field inside a charged sphere (r < R)

let

.