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An electric dipole of length 20 cm havin...

An electric dipole of length 20 cm having `+-3xx10^(-3)` C charge placed at `60^(@)` with respect to a uniform electric field experiences a torque of magnitude 6 Nm. The potential energy of the dipole is

A

`-2sqrt3J`

B

`5sqrt3J`

C

`-3sqrt2J`

D

`3sqrt5J`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, length of dipole 2a = 20 cm `= 2 xx 10^(-2)m` Charge `q = pm 3xx 10^(-3) C, theta = 60^(@)` and torque `tau = 6 N`m
As ` tau = pE sin theta`
or `E = (tau)/(p sin theta) =(tau)/(q(2a)sintheta) " "(because p = q(2a))`
`therefore " " E = (6)/(3 xx 10^(-3) xx 20 xx 10^(-2) xx sin 60^(@)) = (10^(5))/(5sqrt(3) N C^(-1)`
Potetial enegy of diople `U = - p E cos theta - q (2a) Ecos theta = - 3 xx 10^(-3) (20 xx 10^(-2)) (10)/(5sqrt(3)) cos 60^(@)`
` = (3 xx 10^(-5) xx 20 xx 10^(5))/(5sqrt(3) xx 2) = -2sqrt(3)J`
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