Question

Four idenbtial charges `+50 mu C` each are placed, one at each corner of a square of side `2 m`. How much external energy is required to bring another charge of `+50 mu C` from infinity to the centre of the square
(Given `(1)/(4pi epsilon_(0)) = 9 xx 10^(9)(Nm^(2))/(C^(2)))`
A. `64 J`
B. `41 J`
C. `16 J`
D. `10 J`

Answer 1

Correct Answer - A
Potential at the centre of square
`V = 4 xx ((9 xx 10^(9) xx 50 xx 10^(-6))/(2//sqrt(2))) = 90 sqrt(2) xx 10^(4) V`
Work done in bringing a charge `(q = 50 mu C)` from `oo` to centre `(0)` of the square is `W = q (V_(0) - V_(oo)) = q V_(0)`
`rArr W = 50 xx 10^(-6) xx 90 sqrt(2) xx 10^(4) = 64 J`