A dipole with two electric charges of 2 μC magnitude each, with separation distance

Question

A dipole with two electric charges of \(2\ \mu C\) magnitude each, with separation distance \(0.5\ \mu m,\) is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by \(30^\circ\) from the axis, it tends to realign in the direction due to a torque. The value of torque is :

(1) \(5\times 10^{-9}\ Nm\)

(2) \(5\times 10^{-3} \ Nm\)

(3) \(2.5 \times 10^{-12}\ Nm\)

(4) \(2.5\times 10^{-9}\ Nm\)

Answer 1

Correct option is : (1) \(5\times 10^{-9}\ Nm\) 

\(E = \frac{v}{d} = \frac{5}{5\times 10^{-4}} = 10^4V/m\)

\(\tau = PE\ \sin \theta\)

Where \(P = qa = 2 \times 10^{-6} \times 5 \times 10^{-7}\)

\( = 1\times 10^{-12}C-m\)

\(\tau = 1 \times 10^{-12} \times 10^4 \times \frac{1}{2} = 5 \times 10^{-9}\ N-m\)