Question

An electric dipole, made up of positive and negative charges each of $3.5\, \mu C$ and placed at a distance $4.2\, cm$ apart is placed in an electric field of $5.87 \times 10^{5} NC ^{-1}$. What will be the maximum torque which the field can exert on the dipole? Also, obtain the work that must be done to turn the dipole from $0^{\circ}$ to $180^{\circ}$.

• A. $85.26 \times 10^{-3} Nm ^{-1}, 1.70 \times 10^{-1} J$
• B. $75.26 \times 10^{-3} Nm ^{-1}, 1.70 \times 10^{-1} J$
• C. $85.26 \times 10^{-3} Nm ^{-1}, 3.70 \times 10^{-3} J$
• D. $55.26 \times 10^{-3} Nm ^{-1}, 1.70 \times 10^{-3} J$

Answer 1

Answer: (A)

When a dipole is placed in an electric field $E$, force exerted $\tau=p E \sin \theta$, where $p=$ dipole moment and $\theta$ is the angle which makes dipole with the field.
$\tau_{\max }=p E \sin 90^{\circ}$, i.e., $\tau_{\max }=p E$
$\Rightarrow \quad \tau_{\max }=q \times 2 l \times E=\left(3.5 \times 10^{-6}\right) \times 4.2\times 10^{-2} \times 5.8 \times 10^{5}$
$=85.26 \times 10^{-3} Nm ^{-1}$
Work done in rotating the dipole from an angle $\theta_{0}$ to $\theta$,
$W=\int\limits_{\theta_{0}}^{\theta} p E \sin \theta d \theta=p E\left[\cos \theta_{0}-\cos \theta\right]$
$W=p E\left(\cos \theta^{\circ}-\cos 180^{\circ}\right)$
where, $\theta_{0}=0^{\circ}$ and $\theta=180^{\circ}$
$\Rightarrow W=2 p E$
$=2 \times q \times 2 l \times E$
$=2 \times\left(3.5 \times 10^{-6}\right) \times\left(4.2 \times 10^{-2}\right) \times 5.8 \times 10^{5}$
$=1.76 \times 10^{-1} J$