Question

Two charges $+5\mu C$ and $-5\mu C$ separated by $4mm$ form an electric dipole. The dipole is placed in a uniform electric field of $4\times {10}^{5}N/C$ . The work done in rotating the electric dipole through ${180}^o$ , if it starts from the positions of $\theta =0$ is

• A. $4mJ$
• B. $8mJ$
• C. $12mJ$
• D. $16mJ$

Answer 1

Answer: (D)

$16mJ$

The work done in rotating the dipole from stable equilibrium that is when the angle between the electric field and the dipole is zero to the unstable state where the angle between the two is ${180}^{\circ }$

$W=\underset{0}{\overset{180}{\int }}PE\sin \theta$

$W=2PE$

The electric dipole can be calculated by

$P=q\cdot d$

By substituting the values in above equation we get

$P=5\times {10}^{-6}\times 0.004$

$P=2\times {10}^{-8}$

So the work done will be

$W=2\times 2\times {10}^{-8}\times 4\times {10}^5$

$W=16\times {10}^{-3}$

Hence the work done is $16mJ$