An electric dipole of dipole moment is 6.0 × 10⁻⁶ C m placed in a uniform electric field of 1.5 × 10³ NC⁻¹ in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be ___________ m J.

Solution

Physics sir · 4 steps

Work done equals the change in the dipole's potential energy, so compare U at the start and at the end.

1. Potential energy. A dipole at angle θ to a uniform field has U = -pE cos θ. The work you do in turning it slowly is W = U_(final) - Uᵢₙᵢₜᵢₐₗ.
2. Start and end. At the start the dipole is along the field, so θ = 0° and U = -pE. After turning by 180° it points against the field, so U = +pE.

   W = pE - (-pE) = 2pE

3. Put in numbers. W = 2 × 6.0 × 10⁻⁶ × 1.5 × 10³ = 1.8 × 10⁻² J.
4. So. W = 1.8 × 10⁻² J = 18 mJ.

The common slip: 9. Taking the work as pE alone, the energy at only one end, gives 9 mJ. The energy goes from -pE to +pE, a change of 2pE.

The idea to keep. For a dipole in a uniform field, W = pE(cos θ₁ - cos θ₂). Turning it from along the field to against the field always costs 2pE.

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