Question

An electric dipole, made up of positive and negative charges each of $3.5\mu C$ and placed at a distance $4.2cm$ apart is placed in an electric field of $5.87\times 10^{5}N{C}^{-1}$. 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. $85.26\times 10^{-3}N{m}^{-1},1.70\times 10^{-1}J$
• B. $75.26\times 10^{-3}N{m}^{-1},1.70\times 10^{-1}J$
• C. $85.26\times 10^{-3}N{m}^{-1},3.70\times 10^{-3}J$
• D. $55.26\times 10^{-3}N{m}^{-1},1.70\times 10^{-3}J$

Answer 1

Answer: (A)

When a dipole is placed in an electric field $E$, force exerted $\tau =pE\sin \theta$, where $p=$ dipole moment and $\theta$ is the angle which makes dipole with the field.
${\tau }_{\max }=pE\sin 90^{\circ }$, i.e., ${\tau }_{\max }=pE$
$\Rightarrow {\tau }_{\max }=q\times 2l\times E=\left(3.5\times 10^{-6}\right)\times 4.2\times 10^{-2}\times 5.8\times 10^5$
$=85.26\times 10^{-3}N{m}^{-1}$
Work done in rotating the dipole from an angle ${\theta }_0$ to $\theta$,
$W=\underset{{\theta }_0}{\overset{\theta }{\int }}pE\sin \theta d\theta =pE\left[\cos {\theta }_0-\cos \theta \right]$
$W=pE\left(\cos {\theta }^{\circ }-\cos 180^{\circ }\right)$
where, ${\theta }_0=0^{\circ }$ and $\theta =180^{\circ }$
$\Rightarrow W=2pE$
$=2\times q\times 2l\times E$
$=2\times \left(3.5\times 10^{-6}\right)\times \left(4.2\times 10^{-2}\right)\times 5.8\times 10^5$
$=1.76\times 10^{-1}J$