An electric dipole of length 10cm having charges `+- 6xx10^(-3) C`, placed at `30^(@)` with respect to a uniform electric field experiences a torque of magnitude `6 sqrt(3) N-m`. Calculate (i) magnitude of electric field (ii) the potential energy of dipole.

Answer

(i) `2 sqrt(3) xx 10^(4) NC^(-1) , (ii) -18J`

Explanation

Here, `2a = 10cm = 0.1cm, q = +- 6xx10^(-3)C`
`theta = 30^(@) , tau = 6 sqrt(6) N-m, E = ? P.E. = ?`
`:. E = (tau)/(q (2a) sin theta) = (6 sqrt(3))/(6xx10^(-3)x0.1 sin 30^(@))`
`E = 2 sqrt(3) xx 10^(4) NC^(-1)`
`U = -p E cos theta = -q (2a) E cos theta`
`= -6xx10^(-3)xx0.1xx2 sqrt(3) xx 10^(4) cos 30^(@)`
`U = -18 J`