An electric dipole of dipole moment 6 × 10⁻⁶ Cm is placed in uniform electric field of magnitude 10⁶ V / m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _______ J.

Solution

Physics sir · 3 steps

Work done on the dipole is just the change in its potential energy, from -pE up to +pE.

1. Potential energy. A dipole in a uniform field has U = -pE cos θ, where θ is the angle between p⃗ and E⃗. The work you do turning it slowly equals the rise in U.

   W = U_f - Uᵢ = -pE cos 180° - (-pE cos 0°) = 2pE

2. Put in numbers. pE = 6 × 10⁻⁶ × 10⁶ = 6 J, so W = 2 × 6 = 12 J.
3. So. The work needed to turn the dipole from parallel to antiparallel is 12 J.

The common slip: 6. Using only the final energy pE, or stopping the rotation at 90°, gives 6 J instead of 12 J.

The idea to keep. For a dipole, W = pE(cos θ₁ - cos θ₂). Going from 0° to 180° gives 2pE, the largest work any rotation can need.

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