Question

Three charges –q, Q and –q are placed in a straight line maintaining equal distance from each other. What should be the ratio \(\frac {q}{Q}\) so that the net electric potential of the system is zero?

(a) 1

(b) 2

(c) 3

(d) 4

This question was addressed to me in unit test.

My question is taken from Electrostatic Potential due to a Point Charge in portion Electrostatic Potential and Capacitance of Physics – Class 12

Answer 1

Correct answer is (d) 4

To elaborate: Let the distance between any two charges is d. Therefore the net potential energy of the system is\(\frac {-q*Q}{d}+\frac {-q*Q}{d}+\frac {-q*q}{2d}\). But the total energy of the system is zero. So, -qQ-qQ+\(\frac {q^2}{2}\)=0 that means q=4Q, i.e. \(\frac {q}{Q}\)=4.