An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is :

Question

An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is : (A) √(qE/2md)  (B)  2 √(qE/md)  (C) √(2qE/md)  (D) √(qE/md)

Tardigrade Admin · Accepted Answer

moment of inertia (I) = m((d/2))2 ×2 = (md2/2) Now by τ =Iα (qE) (d sinθ) = (md2/2).α α = ((2qE/md)) sinθ for small θ ⇒ α = ((2qE/md))θ ⇒ Angular frequency ω = √(2qE/md)

Q. An electric dipole is formed by two equal and opposite charges $q$ with separation $d$ . The charges have same mass $m$ . It is kept in a uniform electric field $E$ . If it is slightly rotated from its equilibrium orientation, then its angular frequency $ω$ is :

$\frac{qE}{2 m d}$

$2 \frac{qE}{m d}$

$\frac{2 qE}{m d}$

$\frac{qE}{m d}$

moment of inertia (I) $= m (\frac{d}{2})^{2} \times 2 = \frac{m d ^{2}}{2}$
Now by $τ = I α$
$(qE) (d sin θ) = \frac{m d ^{2}}{2} . α$
$α = (\frac{2 qE}{m d}) sin θ$
for small $θ$
$\Rightarrow α = (\frac{2 qE}{m d}) θ$
$\Rightarrow$ Angular frequency $ω = \frac{2 qE}{m d}$

Q. An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is :

2mdqE​​