Dipole in a Uniform External Field

Correct answer: A. Ninety degrees

Explanation: The torque on an electric dipole in a uniform field is τ = pE sin θ, where p is the dipole moment, E is the field magnitude, and θ is the angle between them. For fixed p and E, torque is maximum when sin θ = 1. This occurs at θ = 90°. Therefore option A is correct. At 0° and 180° the torque is zero, while at 60° it is less than the maximum.

Correct answer: A. Dipole moment is parallel or anti-parallel to the field

Explanation: For a dipole in a uniform electric field, torque is given by τ = pE sin θ. It becomes zero when sin θ = 0, which occurs for θ = 0° or 180°. Thus the dipole moment may be parallel or anti-parallel to the field, so option A is correct. A perpendicular position gives maximum torque, and 30° or 60° gives a nonzero torque.

Correct answer: A. Six times

Explanation: The torque on a dipole is τ = pE sin θ. Since the angle is unchanged, sin θ has the same value before and after the change. If p becomes 2p and E becomes 3E, the new torque is τ' = (2p)(3E) sin θ = 6τ. Hence option A, six times, is correct. The factors must be multiplied, not added.