Electrostatic Potential and Potential Energy

Correct answer: C. Negative 21 joule

Explanation: The potential energy of a dipole in a uniform electric field is U = −pE cos θ. Here cos 60° = 1/2, so U = −6 × 7 × 1/2 = −21 J. Therefore option C is correct. The negative sign shows that this orientation has lower energy than the perpendicular orientation; zero would occur at 90°, while −42 J omits the cosine factor.

Correct answer: D. 18 joule

Explanation: Use U = −pE cos θ for the potential energy of a dipole. Since cos 120° = −1/2, U = −4 × 9 × (−1/2) = +18 J. Thus option D is correct. The two negative signs cancel because the angle is obtuse. Zero would require 90°, and 36 J incorrectly ignores the factor of one half.

Correct answer: A. Negative 15√3 joule

Explanation: For a dipole, U = −pE cos θ. The product pE is already given as 30 J, and cos 30° = √3/2. Therefore U = −30 × √3/2 = −15√3 J, making option A correct. The positive value misses the required negative sign, −15 uses the wrong trigonometric value, and zero would be valid only at 90°.