Question

An electric dipole (dipole moment $=p$) is placed in a uniform electric field in stable equilibrium position at rest. Now it is rotated by a small angle and released. The time after which it comes to the equilibrium position again (for first time) is $t$. Then the moment of inertia of the dipole about the axis of rotation is :

• A. $\frac{4t^{2}pE}{3{\pi }^2}$
• B. $\frac{1t^{2}pE}{4{\pi }^2}$
• C. $\frac{2t^{2}pE}{3{\pi }^2}$
• D. $4\frac{t^{2}pE}{{\pi }^2}$

Answer 1

The correct option is D $4\frac{t^{2}pE}{{\pi }^2}$

$T=2\pi \sqrt{\frac{I}{mgL}}$

torque can be also written as $\tau =pE$

$t=\frac{T}{4}=\frac{2\pi }{4}\sqrt{\frac{I}{pE}}$

$I=\frac{4t^2}{{\pi }^2}pE$