A charge +q is carried from point `A( r, 135^(@))` to point `B(r, 45^(@))` following a path, which is a quadrant of circle of radius r ( Fig. 3.97). If the dipole moment is P, find the work done by the external agent (assume short dipole).
.

Options

A. `0`
B. `(1)/(4pi epsilon_(0))(qp)/(r^(2))`
C. `(1)/(4pi epsilon_(0))(sqrt(2)qp)/(r^(2))`
D. `(1)/(4pi epsilon_(0))(qp)/(r )`

Answer

C

Explanation

`V_(A) = (kp cos 135^(@))/(r^(2))`
`V_(B) = (kp cos 45^(@))/(r^(2))`
work done `= q (V_(B) - V_(A))`
`= (1)/(4pi epsilon_(0)) (sqrt(2) pq)/(r^(2))`