Electric Charges and Fields · Question 24

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E0 i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

1. 12 ml2qE0
2. 2 ml2qE0
3. 2 mlqE0
4. 12 2mlqE0

Answer

(2) 2 ml2qE0

Solution

The dipole consists of two charged particles +q and -q, each of mass m, at a distance l2 from the centre.

Moment of inertia about the centre: I = 2m ( l2 )2 = ml22

Dipole moment: p = ql

For a small angular displacement : = -pE0 -qlE0

I d2 dt2 = -qlE0 (angular SHM)

2 = qlE0I = qlE0ml2/2 = 2qE0ml

T = 2 = 2 ml2qE0

Answer: (2)