Two infinitely long straight parallel conductors carrying currents \( I_1 \) and \( I_2 \) are held at a distance d apart in vacuum. The force F on a length L of one of the conductors due to the other is ________________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → proportional to \( I_1 \times I_2 \times L \)
One conductor sets up a field \( B = \mu_0 I_1/2\pi d \) at the other, and a length \( L \) of the second conductor carrying \( I_2 \) feels the force on a current-carrying conductor, \( F = I_2 L B \).
\( \displaystyle F = I_2 L \times \frac{\mu_0 I_1}{2\pi d} = \frac{\mu_0 I_1 I_2 L}{2\pi d} \)
For fixed \( d \), this force is proportional to the product \( I_1 \times I_2 \times L \).
NCERT (2026-27):
Force Between Two Parallel Currents, the Ampere – “… We label this force as Fba, the force on a segment L of ‘b’ due to ‘a’. The magnitude of this force is given by Eq. (4.4),
\( \displaystyle F_{ba} = I_b L B_a = \frac{\mu_0 I_a I_b}{2\pi d}\,L \qquad (4.17) \)”