Question

Two charges q and -4q are held at a separation r on a frictionless surface. Another charge is kept in such a way that they do not move if released. The value of the third charge and its position from -4q is:

• A. -2q, 2r
• B. -4q, 2r
• C. q, r
• D. 4q, 2r

Answer 1

The correct option is B -4q, 2r

$F=\frac{1}{4\pi {ϵ}_0}\frac{q\times 4q}{r^2}$

now,

$F^1=\frac{1}{4\pi {ϵ}_0}\times \frac{4q\times q}{R^2}$

$F-F^1=\frac{1}{4\pi q}4q(\frac{q}{r^2}-\frac{4^1}{R^2})=0$

or, $q^1=-4q$

and $R=2r$

hence, the force is repulsion.