An electric dipole of length 4 cm 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 a charge of ± 8nC.

Sure, here are the steps to solve the problem:

Step 1: First, we need to calculate the electric dipole moment (p). The electric dipole moment is given by the product of the charge (q) and the separation between the charges (2a). In this case, q = 8nC = 8 x 10^-9 C and 2a = 4 cm = 4 x 10^-2 m. So, p = q * 2a = 8 x 10^-9 C * 4 x 10^-2 m = 3.2 x 10^-11 C.m.

Step 2: Next, we calculate the electric field (E). The torque (τ) experienced by a dipole in a uniform electric field is given by τ = p * E * sinθ, where θ is the angle between the dipole moment and the electric field. Rearranging for E, we get E = τ / (p * sinθ). Substituting the given values, τ = 4√3 Nm, θ = 60°, and p = 3.2 x 10^-11 C.m, we get E = 4√3 Nm / (3.2 x 10^-11 C.m * sin60°) = 1.1547 x 10^12 N/C.

Step 3: Finally, we calculate the potential energy (U) of the dipole. The potential energy of a dipole in a uniform electric field is given by U = -p * E * cosθ. Substituting the calculated and given values, we get U = -3.2 x 10^-11 C.m * 1.1547 x 10^12 N/C * cos60° = -1.85 x 10^-2 J.

So, the potential energy of the dipole is -1.85 x 10^-2 J.