What changes occur in the kinetic and potential energies of a moving…

The correct answer is Option (1) → Kinetic energy decreases, potential energy increases

Two electrons repel each other. The potential energy of two charges, \( U=kq_1q_2/r \), is positive for like charges. It grows as the distance \( r \) decreases. The electrostatic force is conservative, so the total energy (kinetic + potential) stays constant.

Option (1) Kinetic energy decreases, potential energy increases — Correct. As the moving electron comes closer, the repulsion acts against its motion and slows it down, so its kinetic energy falls. The work done against the repulsion is stored as electrostatic potential energy, which rises as \( r \) decreases.

Option (2) Both decrease — Incorrect. The total energy of the two electrons is conserved. So a loss of kinetic energy must appear as a gain of potential energy, and both cannot fall together.

Option (3) Both increase — Incorrect. No outside agent supplies energy here, so a gain in one form can only come from the other form.

Option (4) Kinetic energy increases, potential energy decreases — Incorrect. This happens when unlike charges approach. The attraction speeds the charge up, and the (negative) potential energy falls. Between two electrons the force is repulsive.

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. Thus, the potential energy of a system of two charges q₁ and q₂ is”

    \( \displaystyle U=\frac{1}{4\pi\varepsilon_0}\,\frac{q_1q_2}{r_{12}} \qquad (2.22) \)

“… If q₁q₂ > 0, potential energy is positive. This is as expected, since for like charges (q₁q₂ > 0), electrostatic force is repulsive and a positive amount of work is needed to be done against this force to bring the charges from infinity to a finite distance apart.”