An electric dipole, made up of a positive and a negative charge, each of 1 µC and placed at a distance 2 cm apart, is placed in an electric field 10⁵ N/C. Compute the maximum torque which the field can exert on the dipole, and the work that must be done to turn the dipole from a position θ = 0° to θ = 180°

4 × 10⁻³ N-m or Joule

The torque exerted by an electric field E on a dipole of moment p is given by

$\tau=p E \sin \theta$

Where $\theta$ is the angle which the dipole is making with the field. $\tau$ is a maximum, when $\theta=90^{\circ}$. That is

∴ $\tau_{\max }=pE$

Here $p=q(2 \ell)=1 \times 10^{-6} \times 0.02 C / m$ and $E=10^5 N / C$

∴ $\tau_{\max }=1 \times 10^{-6} \times 0.02 \times 10^5=2 \times 10^{-3} N-m$

The work done in rotating the dipole from an angle $\theta_0$ to $\theta$ is given by

$W=\int\limits_{\theta_0}^\theta p E \sin \theta d \theta=p E\left(\cos \theta_o-\cos \theta\right)$

Here $\theta_0=0^{\circ}$ and $\theta=180^{\circ}$

∴ $W=pE\left(\cos 0^{\circ}-\cos 180^{\circ}\right)=2 pE=4 \times 10^{-3}$ N-m or Joule