Question

An electric dipole of moment $p$ is Iying along a uniform electric field $E$. The work done in rotating the dipole by $90^{\circ}$ is

• A. $\sqrt 2 p E$
• B. $\frac{ p E}{ 2}$
• C. $2 \,pE$
• D. $pE$

Answer 1

Answer: (D)

$pE$

Answer 2

When an electric dipole is placed in an electric field $E$, a torque $\tau=p \times E$ acts on it. This torque tries to rotated the dipole through an angle $\theta$. If the dipole is rotated from an angle $\theta_{1}$ to $\theta_{2}$, then work done by external force is given by $W=p E\left(\cos \theta_{1}-\cos \theta_{2}\right)$ Putting $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$ in the E (i), we get $W=p E\left(\cos 90^{\circ}-\cos 90^{\circ}\right)$ $= pE (1-0)$ $= pE$