List-I gives the net electric force on a charge in four arrangements of charges of equal magnitude \(q\). Take \(F=q^{2}/4\pi\varepsilon_0a^{2}\).
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) On \(+q\) at the mid-point of a line of length \(2a\), with \(+q\) at one end and \(-q\) at the other end | (I) \(\sqrt{2}\,F\) |
| (B) On \(+q\) at one corner of a square of side \(a\), with \(+q\) at each of the two neighbouring corners and no charge at the fourth corner | (II) \(3F/4\) |
| (C) On the end charge of three charges \(+q\), \(+q\), \(+q\) placed in that order on a straight line, with a gap \(a\) between neighbours | (III) \(2F\) |
| (D) On the end charge \(+q\) of three charges \(+q\), \(+q\), \(-q\) placed in that order on a straight line, with a gap \(a\) between neighbours | (IV) \(5F/4\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
By the superposition principle, the net force on a charge is the vector sum of the forces from the other charges. Each of these forces is found from Coulomb’s law alone. A charge at distance \( a \) exerts a force \( F \), and one at distance \( 2a \) exerts \( F/4 \).
(A) On \( +q \) at the mid-point, with \( +q \) at one end and \( -q \) at the other end — This matches (III) \( 2F \). Both charges are at distance \( a \). The \( +q \) pushes the middle charge towards \( -q \), and the \( -q \) pulls it the same way, so the forces add.
\( \begin{aligned} F_{\text{net}} &= F+F \\ &= 2F \end{aligned} \)
(B) On \( +q \) at a corner of the square, with \( +q \) at the two neighbouring corners — This matches (I) \( \sqrt{2}\,F \). The two forces have magnitude \( F \) each and are at right angles.
\( \begin{aligned} F_{\text{net}} &= \sqrt{F^{2}+F^{2}} \\ &= \sqrt{2}\,F \end{aligned} \)
(C) On the end charge of \( +q \), \( +q \), \( +q \) — This matches (IV) \( 5F/4 \). Both other charges repel the end charge in the same direction.
\( \begin{aligned} F_{\text{net}} &= F+\frac{F}{4} \\ &= \frac{5F}{4} \end{aligned} \)
(D) On the end charge \( +q \) of \( +q \), \( +q \), \( -q \) — This matches (II) \( 3F/4 \). The near \( +q \) pushes the end charge away, while the far \( -q \) pulls it back.
\( \begin{aligned} F_{\text{net}} &= F-\frac{F}{4} \\ &= \frac{3F}{4} \end{aligned} \)
NCERT (2026-27):
Forces Between Multiple Charges – “Experimentally, it is verified that force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition.”