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

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 $F_{n e t}=0$

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 $\Theta=\frac{n}{2}$ $\tau=P E=$ 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.
Dipole in Non-Uniform Electric field- In case the Electric field is non-uniform, the magnitude of the force on $+q$ and $-q$ will be different. So $F(n e t) \neq 0$ and At the same time due to a couple of forces acting, a torque will also be acting on it.