A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, 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° from the axis, it tends to realign in the direction due to a torque. The value of torque is:

Solution

Physics sir · 3 steps

Get the field from V over d, the dipole moment from q times separation, then torque is pE sin 30°.

1. Field between plates. The field between the plates is uniform: E = V/d = 5/(0.5 × 10⁻³) = 1 × 10⁴ V m⁻¹.
2. Dipole moment. p = q × (2a) = (2 × 10⁻⁶) × (0.5 × 10⁻⁶) = 1 × 10⁻¹² C m.

   τ = pE sin θ = (1 × 10⁻¹²)(1 × 10⁴)sin 30°

3. So. τ = 10⁻⁸ × 0.5 = 5 × 10⁻⁹ N m. That is option (d).

The idea to keep. Torque on a dipole needs the field E, not the voltage. For parallel plates convert first with E = V/d, then use τ = pE sin θ.

Answer from the NTA final answer key. Solution by PrepWiser.