Question

The workdone in rotating a dipole of dipole moment $P$ in electric field from an initial angle ${\theta }_1$ with field to final angle ${\theta }_2$ with field is (symbols have usual meaning)

• A. $W=PE(\cos {\theta }_1-\cos {\theta }_2)$
• B. $W=-PE(\cos {\theta }_1-\cos {\theta }_2)$
• C. $W=PE(\cos {\theta }_1+\cos {\theta }_2)$
• D.
  $W=-PE(\sin {\theta }_1-\sin {\theta }_2)$

Answer 1

The correct option is A $W=PE(\cos {\theta }_1-\cos {\theta }_2)$

Work done during rotation is
$W={\int }_{{\theta }_1}^{{\theta }_2}\tau d\theta [\because \tau =PE\sin \theta ]$

$W=[-PE\cos \theta {]}_{{\theta }_1}^{{\theta }_2}$

$\therefore W=PE(\cos {\theta }_1-\cos {\theta }_2)$