Question

An electric dipole consists of point charges $-1.0 \, \mathrm{pC}$ and $+1.0 \, \mathrm{pC}$ located at $(0, 0)$ and $(3 \, \mathrm{mm}, 4 \, \mathrm{mm})$ respectively in the $x$–$y$ plane. An electric field $\vec{E} = \left( 1000 \, \mathrm{V/m} \right) \, \hat{i}$ is switched on in the region. Find the torque $\vec{\tau}$ acting on the dipole.
 

Hint:

To solve torque problems for dipoles, always determine the displacement vector, dipole moment, and relative orientation with the electric field.

Answer 1

The torque \(\tau\) is given by: 

 \[ \tau = pE \sin \theta \] This can be written as: \[ \tau = (2aq) E \sin \theta \] Substituting the known values: \[ \tau = \left(5 \times 10^{-3} \times 1 \times 10^{-12} \times 10^3\right) \times \frac{4}{5} \] Simplifying: \[ \tau = 4 \times 10^{-12} \, \text{Nm} \] The direction of the torque is along the negative \(Z\)-direction.