Torque On An Electric Dipole In A Uniform Electric Field - Practice Questions & MCQ

Net Force-  

When a dipole is kept in a uniform electric field. The net force experienced by the dipole is zero as shown in the below figure.

I.e $F_{\text {net }}=0$

Hence dipole will not make any linear motion.

Torque on dipole-

Net torque about the center of dipole is given as $\tau=Q E d \sin \theta$
Using $P=Q d_{\text {we get }} \tau=P E \sin \theta$
So $\vec{\tau}=\vec{P} \times \vec{E}$
- The direction of the torque is normal to the plane containing dipole moment $P$ and electric field $E$ and is governed by right-hand screw rule.
- If Dipole is parallel to E the torque is Zero. I.e $\Theta=0^{\circ} \quad \tau=0$ (This is the position of stable equilibrium of dipole)

• Torque is maximum when Dipole is perpendicular to E. I.e ${ }^{\Theta}=\frac{\pi}{2} \quad \tau=P E=$ maximum torque

Oscillation of dipole -If a dipole experiencing a torque in an electric field is allowed to rotate, then it will rotate to align itself to the Electric field. But when it reaches along the direction of E the torque becomes zero. But due to inertia, it overshoots this equilibrium condition and then starts oscillating about this mean position.

The time period of this oscillation is given as

$
T=2 \pi \sqrt{\frac{I}{P E}}
$

where $\mathrm{I}=$ moment of inertia of dipole about the axis passing through its center and perpendicular to its length.