An electric dipole of mass m,charge q,and len | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The torque acting on the dipole in an electric field is $	au = p E_0 \sin 	heta$. For small oscillations,$\sin 	heta \approx 	heta$,so $	au =

Vedclass · Accepted Answer

$2 \pi \sqrt{\frac{m l}{2 q E_0}}$

Vedclass · Answer

(D) The torque acting on the dipole in an electric field is $	au = p E_0 \sin 	heta$. For small oscillations,$\sin 	heta \approx 	heta$,so $	au = p E_0 	heta$. Since $p = q l$,we have $	au = q l E_0 	heta$. The restoring torque is $	au = -I \alpha$,where $I$ is the moment of inertia about the center of mass. For a dipole of two point masses $m/2$ at distance $l/2$ from the center,$I = 2 	imes (m/2) 	imes (l/2)^2 = \frac{m l^2}{4}$. Equating the magnitudes,$I \frac{d^2 	heta}{dt^2} = -q l E_0 	heta$. Comparing with the $SHM$ equation $\frac{d^2 	heta}{dt^2} + \omega^2 	heta = 0$,we get $\omega^2 = \frac{q l E_0}{I} = \frac{q l E_0}{m l^2 / 4} = \frac{4 q E_0}{m l}$. Wait,re-evaluating the moment of inertia: If the dipole consists of two masses $m$ at ends,$I = 2 m (l/2)^2 = \frac{m l^2}{2}$. Then $\omega^2 = \frac{q l E_0}{m l^2 / 2} = \frac{2 q E_0}{m l}$. The time period $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{m l}{2 q E_0}}$.

An electric dipole of mass $m$,charge $q$,and length $l$ is placed in a uniform electric field $\vec{E} = E_0 \hat{i}$. When the dipole is rotated slightly from its equilibrium position and released,the time period of its oscillations will be:

Similar Questions

$A$ given charge situated at a distance $r$ from an electric dipole on its axis experiences a force $F$. If the distance of the charge from the dipole is doubled,the force acting on the charge will be

Two charges $+q$ and $-q$ are kept at a certain distance apart. Then, at any point on the right bisector of the line joining the two charges:

What does an electric dipole experience when placed in a uniform electric field?

When does the torque acting on an electric dipole in a uniform electric field become zero?

The electric field due to a dipole at a distance $r$ on its axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module