Question

Two equal like charges are placed on the vertices of an equilateral triangle . What charge must be placed on the third vertex so that the total potential energy is zero

Answer 1

To make the net potential energy of the system zero the charge placed should be equal to half the magnitude and of opposite sign of the other two charges placed.

Explanation :

Let the two charges have a magnitude of q and the third charge has a magnitude of q'. let the side of the triangle be r.

Hence net potential energy of the system,

P = (q²/r  + qq'/r  + qq'/r)/4πε₀

Since the potential energy of the system should be zero, hence

(q²/r  + qq'/r  + qq'/r)/4πε₀ = 0

=> q² + 2qq' = 0

=> q + 2q' = 0

=> q' = -q/2

Hence to make the net potential energy of the system zero the charge placed should be equal to half the magnitude and of opposite sign of the other two charges placed.

Answer 2

Answer:-q/2

Explanation: