Question

two charges q and -3q are fixed on x-axis separated by distance d. where should a third charge 2q be placed from A such that it will not experience any force?

Answer 1

Suppose the third charge is placed at P.

For the force experienced by the third at P to be zero, the net electric field at P must be zero.

From the diagram, the net field at P is,

E = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2

=> 0 = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2

=> 0 = 4/(0.2 + x)2 - 1/x2

=> 1/x2 = 4/(0.2 + x)2

=> 1/x = 2/(0.2 + x)

=> 0.2 + x = 2x

=> x = 0.2 m