Two point charges -4 μ c and 4 μ c, constituting an electric dipole, are placed at (-9,0,0) cm and (9,0,0) cm in a uniform electric field of strength 10⁴ NC⁻¹. The work done on the dipole in rotating it from the equilibrium through 180° is :

Solution

Physics sir · 4 steps

A 180° turn from equilibrium takes the dipole from its lowest energy to its highest, so W = 2pE.

1. Dipole moment. The charges sit 18 cm apart, so 2a = 0.18 m. Then p = q × 2a = 4 × 10⁻⁶ × 0.18 = 7.2 × 10⁻⁷ C m.
2. Work from energies. The potential energy of a dipole in a uniform field is U = -pE cos θ. The work done in rotating it equals the rise in this energy.

   W = U_(180°) - U_(0°) = pE - (-pE) = 2pE

3. Put in numbers. W = 2 × 7.2 × 10⁻⁷ × 10⁴ = 1.44 × 10⁻² J.
4. So. W = 14.4 mJ, which is option (d).

The idea to keep. For a dipole in a uniform field, work done in turning it is pE(cos θ₁ - cos θ₂). From equilibrium to 180°, that is 2pE. Always use the full separation 2a in p.

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