Which of the following statements are true?(A) The potential energy f…

The correct answer is Option (1) → (B) and (D) only

The potential energy of two point charges separated by \( r \) is

    \( \displaystyle U = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r} \)

Its sign is the sign of the product \( q_1 q_2 \).

(A) The potential energy for a system of two negative point charges is negative — Incorrect. For two negative charges the product \( q_1 q_2 \) is positive, so \( U \) is positive.

(B) Electrostatic force is a conservative force — Correct. The work done by the electrostatic force between two points does not depend on the path, which is why a potential energy can be defined for it.

(C) Negative potential energy between two charges implies that the force between them is repulsive — Incorrect. \( U \lt 0 \) means unlike charges, and unlike charges attract: work must be done to pull them apart.

(D) Electrostatic potential energy is a scalar quantity — Correct. Energy has magnitude only, so the potential energies of pairs of charges are simply added.

Statements (B) and (D) are correct, which is Option (1).

NCERT (2026-27):
Potential Energy of a System of Charges – “… Since electrostatic force is conservative, this work gets stored in the form of potential energy of the system.”

Potential Energy of a System of Charges – “… If q₁q₂ > 0, potential energy is positive. … For unlike charges (q₁q₂ < 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.”