B

Step 1: Understand that a dipole in an electric field experiences torque. The torque \( \tau \) on a dipole moment \( \mathbf{p} \) in an electric field \( \mathbf{E} \) is given by the formula: \( \tau = \mathbf{p} \times \mathbf{E} \).

Step 2: The magnitude of the torque can also be expressed as: \( \tau = pE \sin\theta \), where \( \theta \) is the angle between the dipole moment and the electric field.

Step 3: Since we require the torque needed to rotate the dipole from the stable equilibrium position, we conclude that the torque required to rotate the dipole by an angle \( \theta \) is \( pE \sin\theta \).

Therefore, the correct answer is Option B: \( pE \sin\theta \).