An electric dipole of moment p = 5 × 10⁻⁶ C·m is initially aligned with a uniform electric field E = 4 × 10⁵ N/C. It is rotated to 60° relative to the field. Find the change in potential energy.
Options

Question

An electric dipole of moment p = 5 × 10⁻⁶ C·m is initially aligned with a uniform electric field E = 4 × 10⁵ N/C. It is rotated to 60° relative to the field. Find the change in potential energy.

Options

G1 Physics · Accepted Answer

Step 1: Potential energy of a dipole in a field is U = −pEcosθ. Step 2: Initial angle θᵢ = 0°, final angle θ𝒇 = 60°. Step 3: Change ΔU = U𝒇 − Uᵢ = −pEcos60° + pEcos0° = pE(1 − 1/2). Step 4: pE = (5 × 10⁻⁶)(4 × 10⁵) = 2 J. Step 5: ΔU = 2 × 1/2 = 1.0 J (positive because the dipole moves away from its lowest-energy alignment). Final answer: +1.0 J, Option B.