JEE Main 2023 · 13 April · morning · Single correct · +4 / −1

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field 'E⃗' of 10 dyne/C making 30° angle with E⃗, the magnitude of torque acting on dipole is:

  1. (a) 4 · 0 × 10⁻¹⁰ Nm
  2. (b) 1.5 × 10⁻⁹ Nm
  3. (c) 1.0 × 10⁻⁸ Nm
  4. (d) 2.0 × 10⁻¹⁰ Nm
Answer and solution

Answer (d) 2.0 × 10⁻¹⁰ Nm

Solution

Physics sir · 3 steps

Turn dyne/C into N/C first, then torque is just pE sin θ.

  1. Dipole moment. p = q × 2a = 0.01 × 0.4 × 10⁻³ = 4 × 10⁻⁶ C m.
  2. Field in SI. 1 dyne = 10⁻⁵ N, so E = 10 × 10⁻⁵ = 10⁻⁴ N C⁻¹.

    τ = pE sin θ = 4 × 10⁻⁶ × 10⁻⁴ × sin 30°

  3. So. τ = 4 × 10⁻¹⁰ × 1/2 = 2.0 × 10⁻¹⁰ N m, which is option (d).

The idea to keep. Torque on a dipole is pE sin θ, largest at 90° and zero when the dipole is along the field. Always bring CGS units like dyne into SI before multiplying.

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

Study Electrostatics I — Charges, Field & Gauss's Law

Asked about 150 times in JEE Main since 2020. This question is from 2023.