Final answer:
The torque on the dipole is zero when the dipole moment vector 'p' is either parallel or antiparallel to the electric field 'E', which corresponds to angles of 0 or 180 degrees from the electric field direction.
Step-by-step explanation:
The orientations of the dipole for which the torque on the dipole is zero, measured counterclockwise from the electric field direction, occur when the dipole is aligned either parallel or antiparallel to the electric field. In a uniform electric field, the net force on the dipole is zero, but there can be torque that tends to rotate the dipole to align with the field. The torque (τ) experienced by an electric dipole in a uniform electric field (E) is given by τ = p × E, where 'p' is the dipole moment and 'E' is the electric field vector. The torque will be zero when the angle between p and E is either 0 degrees (parallel) or 180 degrees (antiparallel) because the cross product of two vectors is zero when the vectors are parallel to each other. In these orientations, the dipole does not experience any rotation as a result of the electric field.