Two point charges (Q each are placed at (0,y) and (0-y) A point charge q of the same polarity can move along the x-axis. Then

Options

A. The force on q is maximum at `x = pm y// sqrt(2)`
B. The charge q is in equilibrium at the origin
C. The charge q performs an oscillatory motion about the origin
D. For any position of q other then origin the force is directed away from origin

Answer

A, B, D

Explanation

At a point with coordinates (x, 0) the force on charge is given as `F=q ((k(2Q)x)/(x^2+y^2)^(3//2))`
Thus for F to be maximum, we solve for `dF//dx = 0 `which gives `x pm y/sqrt2`
The charge is in equilibrium at the origin where net electric field due to the two charges is zero. However, the equilibrium is not stable since the force is repulsive along x direction and it will not be able to restore the charge at the origin. The charge therefore cannot perform oscillatory motion. Thus options (A), (B) and (D) are correct.