Question

If we rotate the dipole of moment $p$ placed in an electric field $E$ from an ${\theta }_1$ to ${\theta }_2$, the work done by the external force is

• A. $pE(\cos {\theta }_2-\cos {\theta }_1)$
• B. $pE(\cos {\theta }_1-\cos {\theta }_2)$
• C. $pE(\sin {\theta }_2-\sin {\theta }_1)$
• D. $pE(\sin {\theta }_1-\sin {\theta }_2)$

Answer 1

The correct option is B $pE(\cos {\theta }_1-\cos {\theta }_2)$

Given dipole of dipole moment $p$ in an electric field $E$. It is rotated from ${\theta }_1$ to ${\theta }_2$. We have to find the work done by external force.

When a dipole of dipole moment $p$ is placed in electric field, work done in rotated the dipole by angle $\theta$ is

$W=-pE\cos {\theta }_1$

Now work done in rotating dipole by ${\theta }_1$ is

$W_2=-pE\cos {\theta }_2$

Work done in rotating the dipole from ${\theta }_1$ to ${\theta }_2$ is

$W=W_2-W_1$

$=-pE\cos {\theta }_2-(-pE\cos {\theta }_1)$

$=pE(\cos {\theta }_1-\cos {\theta }_2)$