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 $t$. If the moment of inertia of the dipole about the axis of rotation is $x\frac{t^{2}pE}{{\pi }^2},$ then $x$ is:

• A. $4$
• B. $2$
• C. $8$
• D. $1$

Answer 1

The correct option is A $4$

Time period for the dipole oscillations is $T=\frac{2\pi }{\sqrt{\frac{pE}{I}}}$
Time for first equilibrium condition is $t=\frac{T}{4}$
or,$t=\frac{2\pi }{4}\sqrt{\frac{I}{pE}}$
or, $I=\frac{4t^2}{{\pi }^2}pE$
Therefore, $x=4$