Question

+4q and -q are two charges separated by a distance ‘d’ metre. Where should be a third charge +Q be placed to attain equilibrium

Answer 1

Given : +4q and -q are two charges seperated by a distance d metre.

To find : The position of third charge +Q for which it attains equilibrium.

solution : as first and 2nd charges are opposite in nature so equilibrium will be happen when third charge is placed near the 2nd charge -q. +Q is located x distance from -q.

(+4q)-------------(-q) -----x-----(+Q)

at equilibrium,

force due to +4q on +Q = force due to -q on +Q

⇒k(4q)(Q)/(d + x)² = kqQ/x²

⇒4/(d + x)² = 1/x²

⇒(d + x)/x = ± 2

⇒d + x = ± 2x

⇒d = - x ± 2x = -x + 2x or -x - 2x

but negative of x is not possible. because x is length and length can't be negative.

so, d = x

Therefore the third charge +Q is placed d distance from the -q and 2d distance from +4q