Three charges \( -q, Q \) and \( -q \) are placed in a straight line such that \( Q \) is in the middle of the other two charges. If the potential energy of the system of these charges is zero, then the ratio \( Q:q \) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1:4 \)
The potential energy of a system of point charges is the sum of \( kq_iq_j/r_{ij} \) over every pair.
Let the distance between \( Q \) and each outer charge be \( r \); the two outer charges are then \( 2r \) apart.
\( \displaystyle U = k\left[\frac{(-q)(Q)}{r} + \frac{(Q)(-q)}{r} + \frac{(-q)(-q)}{2r}\right] \)
\( \displaystyle U = \frac{k}{r}\left[-2qQ + \frac{q^{2}}{2}\right] \)
Putting \( U = 0 \):
\( \displaystyle 2qQ = \frac{q^{2}}{2} \Rightarrow Q = \frac{q}{4} \)
\( Q:q = 1:4 \)