An electric dipole of length 4cm when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4√3 Nm. Calculate the potential energy of the dipole if it has charge ±8nC.

Dipole moment (P) = q × 2l
P = 8 × 10⁻⁹ × 2 × 4 × 10⁻² = 64 × 10⁻¹¹ Cm
Torque on the dipole in a uniform electric field
τ = PEsinθ
E = τ/(Psinθ)
Potential energy of the dipole is
U = -PEcosθ
On substituting the value, we get the value of E and U
U = -P(τ/(Psinθ))cosθ = -τ(cosθ/sinθ) = -τtanθ
U = -4√3 Nm × tan60° = -4√3 Nm × √3 = -12 Nm