The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are :
(i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image.
Now system consists of two charge +q an -q at seperation`2d`. If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is `2y`

The force between point charge +q and earthed conducting plane is

Options

A. `(1)/(4pi in_(0)) q^(2)/d^(2)` (repulsive)
B. `(1)/(4pi in_(0)) q^(2)/d^(2)` (attractive)
C. `(1)/(4pi in_(0)) q^(2)/(4d^(2))` (repulsive)
D. `(1)/(4pi in_(0)) q^(2)/(4d^(2))` (attractive)

Answer

D

Explanation

As given in paragraph, it is treated as `+q` and `-q` point charge at a distance `2a`
`F=1/(4pi in_(0))((-q)(q))/((2d)^(2))`