Question

Two isolated metallic spheres, one with a radius R and another with a radius 5R, each carries a charge ‘q’ uniformly distributed over the entire surface. Which sphere stores more electric potential energy?

(a) The sphere with radius 5R

(b) Both of the spheres will have the same energy

(c) The sphere with radius R

(d) Initially it will be the sphere with radius 5R then it will shift to the sphere with radius R

This question was posed to me in an interview for job.

This interesting question is from Potential Energy in an External Field in division Electrostatic Potential and Capacitance of Physics – Class 12

Answer 1

Right option is (c) The sphere with radius R

The best explanation: The sphere with radius R stores more electric potential energy. According to the electric potential energy equation  → U = \(\frac {1}{(4\pi \varepsilon_o)} \times [ \frac {q_1q_2}{r} ]\)

Potential energy is inversely proportional to radius. Therefore, the sphere with lesser radius will store more energy. So, the smaller sphere will store more energy.