An electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electr

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Question

An electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through 60° with respect to the electric field. The change in potential energy of the dipole is:

Accepted Answer

Correct Answer: C — 1.0 JStep-by-step Solution:Potential energy of an electric dipole: U = −PE cosθInitial state (θ₁ = 0°): U₁ = −PE cos0° = −PE = −(5 × 10⁻⁶)(4 × 10⁵) = −2 JFinal state (θ₂ = 60°): U₂ = −PE cos60° = −PE × (1/2) = −1 JChange in PE: ΔU = U₂ − U₁ = −1 − (−2) = +1.0 JAlternatively: ΔU = PE(cosθ₁ − cosθ₂) = PE(cos0° − cos60°) = PE(1 − 1/2) = PE/2 = 2/2 = 1.0 JWhy Option A (1.5 J) is wrong: Would require cosθ₁ − cosθ₂ = 3/4, which is not the case for θ₁ = 0° and θ₂ = 60°.Why Option B (0.8 J) is wrong: No standard trigonometric computation with these angles and values gives 0.8 J.Why Option D (1.2 J) is wrong: Similarly, 1.2 J does not correspond to any correct calculation here.Key Concepts from Electrostatic Potential and Capacitance (NCERT Class 12, Chapter 2):Potential energy of a dipole: U = −PE cosθ = −P · E. Minimum (most stable) at θ = 0°; maximum at θ = 180°.Torque on a dipole: τ = PE sinθ = P × E. Maximum at θ = 90°; zero at θ = 0° and 180°.Work done in rotating from θ₁ to θ₂: W = PE(cosθ₁ − cosθ₂) = ΔU (work done against the field).Electric field due to a dipole: on axial line: Eax = 2P/(4πε₀r³); on equatorial line: Eeq = P/(4πε₀r³). The axial field is twice the equatorial field at the same r.

An electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through 60° with respect to the electric field. The change in potential energy of the dipole is:

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An electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through 60° with respect to the electric field. The change in potential energy of the dipole is:

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