Question

Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu \mathrm{C} / \mathrm{m}^{2}$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is:

• A. 112 Nm
• B. 1.12 Nm
• C. 2.24 Nm
• D. 11.2 Nm

Hint:

The torque acting on a dipole in an electric field is given by the product of the dipole moment and the electric field.

Answer 1

The Correct Option is B

1. Electric field due to the charge sheet: \[ E = \frac{\sigma}{2 \epsilon_0} \]
2. Torque acting on the rod: \[ \tau = PE \sin \theta \] \[ \tau = \left[ 2 \times 10^{-6} \times \frac{2}{10} \right] \left[ \frac{100 \times 10^{-6}}{2 \times 8.85 \times 10^{-12}} \right] \frac{1}{2} \] \[ \tau = \frac{10}{8.85} = 1.12 \mathrm{~Nm} \] Therefore, the correct answer is (2) 1.12 Nm.