Electrostatic Potential and Potential Energy

Correct answer: A. Zero

Explanation: For a dipole in a uniform field, potential energy is U = −pE cos θ, where θ is measured from the field direction. In the perpendicular arrangement, θ = 90° and cos 90° = 0. Therefore U = 0, provided the usual reference is used and the field is uniform. This is neither the minimum nor maximum energy; it lies between the parallel and antiparallel values.

Correct answer: A. Cosine

Explanation: The potential energy of an electric dipole in a uniform field is U = −pE cos θ, where θ is the angle between the dipole moment and the electric field. Therefore the cosine of the angle appears directly. The sine function belongs to the torque expression τ = pE sin θ, which is a different physical quantity. Tangent does not occur in either standard relation here.

Correct answer: C. 0 J

Explanation: The governing equation is U = −pE cos θ. In the perpendicular position, the angle between the dipole moment and the electric field is 90°, and cos 90° = 0. Consequently U = −(9)(2)(0) = 0 J. Option C is correct. The values ±18 J would correspond to parallel or antiparallel orientations, while 9 J does not follow from the relation.

Correct answer: C. Positive

Explanation: The dipole potential energy in a uniform electric field is U = −pE cos θ. For an obtuse angle, 90° < θ < 180°, the cosine is negative. The negative sign already present in the formula therefore changes the result to a positive value. At 90° the energy is zero, and for an acute angle it is negative, so the obtuse-angle case is distinctly positive.