Two point charges ±200 μC are placed at a distance of 2 mm from each other in uniform electric field of $10^5 N/C$ such that the line joining the negative to positive charge makes an angle 30° with the field. The torque acting on the system is,
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.02 Nm
Torque on a dipole in a uniform electric field:
$\tau = p E \sin \theta$
Dipole moment: $p = q \cdot d$
Given: $q = 200 \, \mu C = 200 \times 10^{-6} \, C$, $d = 2 \, \text{mm} = 2 \times 10^{-3} \, m$, $E = 10^5 \, N/C$, $\theta = 30^\circ$
$p = 200 \times 10^{-6} \times 2 \times 10^{-3} = 4 \times 10^{-7} \, C\cdot m$
$\tau = 4 \times 10^{-7} \cdot 10^5 \cdot \sin 30^\circ$
$\tau = 4 \times 10^{-7} \cdot 10^5 \cdot 0.5 = 0.02 \, N\cdot m$
Torque $τ = 0.02 N·m$