Consider three long straight parallel wires as shown in the figure. Length of wire B is 25 cm. Choose the correct options.
(A) Net force experienced by wire B is \( 2 \times 10^{-4}\,\mathrm{N} \) towards left
(B) Magnitude of repulsion force by wire A on B is \( 5 \times 10^{-4}\,\mathrm{N} \)
(C) Magnitude of repulsion force by wire C on B is \( 2 \times 10^{-4}\,\mathrm{N} \)
(D) Net force experienced by wire B is \( 2 \times 10^{-4}\,\mathrm{N} \) towards right
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (C) only
The force between two long parallel currents on a length \( l \) is given below; parallel currents attract and antiparallel currents repel.
\( \displaystyle F = \frac{\mu_0 I_1 I_2\,l}{2\pi d} = 2\times10^{-7}\,\frac{I_1 I_2\,l}{d} \)
From the figure: A carries 30 A upward, B carries 10 A downward and C carries 20 A upward; \( AB = 3\,\mathrm{cm} \), \( BC = 5\,\mathrm{cm} \), and \( l = 25\,\mathrm{cm} = 0.25\,\mathrm{m} \). The current in B is opposite to both A and C, so both forces on B are repulsive.
\( \displaystyle F_{AB} = 2\times10^{-7} \times \frac{30 \times 10 \times 0.25}{0.03} = 5\times10^{-4}\,\mathrm{N} \quad \text{(B pushed to the right, away from A)} \)
\( \displaystyle F_{CB} = 2\times10^{-7} \times \frac{20 \times 10 \times 0.25}{0.05} = 2\times10^{-4}\,\mathrm{N} \quad \text{(B pushed to the left, away from C)} \)
\( \displaystyle F_{\text{net}} = 5\times10^{-4} - 2\times10^{-4} = 3\times10^{-4}\,\mathrm{N} \text{ to the right} \)
(A) Net force experienced by wire B is \( 2 \times 10^{-4}\,\mathrm{N} \) towards left — Incorrect. The net force is \( 3\times10^{-4}\,\mathrm{N} \) towards the right.
(B) Magnitude of repulsion force by wire A on B is \( 5 \times 10^{-4}\,\mathrm{N} \) — Correct. This is \( F_{AB} \) found above.
(C) Magnitude of repulsion force by wire C on B is \( 2 \times 10^{-4}\,\mathrm{N} \) — Correct. This is \( F_{CB} \) found above.
(D) Net force experienced by wire B is \( 2 \times 10^{-4}\,\mathrm{N} \) towards right — Incorrect. The direction is right, but the magnitude is \( 3\times10^{-4}\,\mathrm{N} \).
NCERT (2026-27):
Force Between Two Parallel Currents, the Ampere – “… Thus, Parallel currents attract, and antiparallel currents repel. … Let fba represent the magnitude of the force Fba per unit length. Then, from Eq. (4.17),
\( \displaystyle f_{ba} = \frac{\mu_0 I_a I_b}{2\pi d} \qquad (4.19) \)”