If a proton is brought towards an electron from infinity, the potential energy of the system will
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → decrease
A proton and an electron have unlike charges, so they attract each other. The potential energy of the pair is taken as zero when they are infinitely far apart, and at a separation \( r \) it is
\( \displaystyle U = -\frac{e^{2}}{4\pi\varepsilon_0 r} \)
As \( r \) decreases, \( U \) becomes more and more negative, so it decreases. The attractive force does positive work as the particles approach.
Option (1) decrease — Correct. \( U \) falls from zero at infinity to a negative value that becomes larger in size as \( r \) decreases.
Option (2) increase — Incorrect. The potential energy would increase only for like charges, which repel.
Option (3) first increase and then decrease — Incorrect. The force is attractive at every separation, so there is no turning point.
Option (4) remain unchanged — Incorrect. \( U \) depends on \( r \).
NCERT (2026-27):
Potential Energy of a System of Charges – “… For unlike charges (q1q2 < 0), the electrostatic force is attractive. In that case, a positive amount of work is needed against this force to take the charges from the given location to infinity. 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.”