Question

A dipole is placed parallel to the electric field.
If W is the work done in rotating the dipole by 60 degree; then work done by rotating 180 degrees is

Answer 1

Given:

A dipole is placed parallel to the electric field.

W is the work done in rotating the dipole by 60 degree.

To find:

Work done in rotating 180°.

Calculation:

General formula for work done by Dipole in rotation in uniform Electrostatic Field:

$\boxed{ \sf{work = PE \bigg \{ \cos( \theta1) - \cos( \theta2) \bigg \}}}$

While rotating by 60°:

$\sf{W = PE \bigg \{ \cos( 0 \degree) - \cos( 60 \degree) \bigg \}}$

$\sf{ = > W = PE \bigg \{ 1 - \dfrac{1}{2} \bigg \}}$

$\sf{ = > W = PE \bigg \{ \dfrac{1}{2} \bigg \}}$

While rotating by 180°:

$\sf{W2 = PE \bigg \{ \cos( 0 \degree) - \cos( 180 \degree) \bigg \}}$

$\sf{ = > W2 = PE \bigg \{ 1 - ( - 1)\bigg \}}$

$\sf{ = > W2 = 2PE }$

Dividing the two equations:

$\rm{ \therefore \: \dfrac{W2}{W} = 4}$

$\rm{ = > \: W2 = 4W }$

So, final answer is:

$\boxed{ \bold{ \large{ \: W2 = 4W }}}$