Which of the following statements are correct related to electric potential energy?
(A) The electric potential energy is a vector quantity.
(B) The potential energy of two like charges is positive and for two unlike charges, it is negative.
(C) The work done by an electrostatic field in moving a charge from one point to another is independent of the path taken.
(D) The potential energy of an electric dipole in a uniform electric field is maximum, when the dipole moment is opposite to the electric field.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B), (C) and (D) only
The electrostatic force is conservative, so a potential energy can be defined; it is an energy, and energy is a scalar.
(A) The electric potential energy is a vector quantity. — Incorrect. Potential energy is work stored in the system, a scalar; it has a sign but no direction.
(B) The potential energy of two like charges is positive and for two unlike charges, it is negative. — Correct. The sign follows the product \( q_1 q_2 \):
\( \displaystyle U = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r} \)
(C) The work done by an electrostatic field in moving a charge from one point to another is independent of the path taken. — Correct. This is what it means for the electrostatic field to be conservative.
(D) The potential energy of an electric dipole in a uniform electric field is maximum, when the dipole moment is opposite to the electric field. — Correct. The potential energy of a dipole is given below; at \( \theta = 180^\circ \) it reaches its largest value \( +pE \).
\( \displaystyle U = -\vec{p}\cdot\vec{E} = -pE\cos\theta \)
NCERT (2026-27):
Potential Energy of a System of Charges – “… If q1q2 > 0, potential energy is positive. … For unlike charges (q1 q2 < 0), the electrostatic force is attractive. … In other words, a negative amount of work is needed for the reverse path (from infinity to the present locations), so the potential energy is negative.”
Introduction – “… It means that the work done by an electrostatic field in moving a charge from one point to another depends only on the initial and the final points and is independent of the path taken to go from one point to the other.”
Summary – “… The potential energy of a dipole moment p in a uniform electric field E is \( -\mathbf{p}\cdot\mathbf{E} \).”