A total electric charge of 3.5 nC is distributed uniformly over the surface of a metal sphere with a radius of 24 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere: (a) 48.0 cm; (b) 24.0 cm; (c) 12.0 cm.?

Question

Answer

Given:

Total electric charge (Q) = 3.5 nC

Radius (r) = 24 cm

Formula:

Electric potential (V) = kQ/r

where k is the Coulomb constant (9 x 10^9 Nm^2/C^2).

Solution:

(a) Potential at 48.0 cm:

Using the formula, we get:

V = kQ/r = (9 x 10^9 Nm^2/C^2) x (3.5 x 10^-9 C) / (48 x 10^-2 m) = 1.91 V

Therefore, the potential at a distance of 48.0 cm from the center of the sphere is 1.91 V.

(b) Potential at 24.0 cm:

Using the formula, we get:

V = kQ/r = (9 x 10^9 Nm^2/C^2) x (3.5 x 10^-9 C) / (24 x 10^-2 m) = 3.54 V

Therefore, the potential at a distance of 24.0 cm from the center of the sphere is 3.54 V.

(c) Potential at 12.0 cm:

Using the formula, we get:

V = kQ/r = (9 x 10^9 Nm^2/C^2) x (3.5 x 10^-9 C) / (12 x 10^-2 m) = 7.89 V

Therefore, the potential at a distance of 12.0 cm from the center of the sphere is 7.89 V.

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