Question

There are two charges → Q1 = +q and charge Q2 = +2q. From the initial point (Q), Q1 is at a distance of r and Q2 is at a distance 2r. Which charge (Q1 or Q2) will have higher electrostatic potential energy?

(a) Q1

(b) Both will have the same energy

(c) Q2

(d) The information given is not enough to determine

I have been asked this question in a national level competition.

This intriguing question comes from Potential Energy in an External Field topic in division Electrostatic Potential and Capacitance of Physics – Class 12

Answer 1

The correct option is (b) Both will have the same energy

The best I can explain: Electrostatic potential energy of Q1 → U1 = \(\frac {1}{(4\pi \varepsilon_o)}\) × [Q × \(\frac {q}{r}\)] ……….1

Electrostatic potential energy of Q2 → U2 = \(\frac {1}{(4\pi \varepsilon_o)}\) × [Q × \(\frac {2q}{2r}\)]

→ U2 = \(\frac {1}{(4\pi \varepsilon_o)}\) × [Q x \(\frac {q}{r}\)] ………2

1 = 2

Therefore, both the charges will have the same energy.