Two parallel conducting wires, A and B, of equal length, carry currents I and 20I, respectively, in the same direction, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A and B will attract each other with the same force
Currents in the same direction attract, and the force on a length L of either wire is
\( \displaystyle F = \frac{\mu_0 I_1 I_2 L}{2\pi d} = \frac{\mu_0 (I)(20I) L}{2\pi d} \)
The expression is the same for both wires: the forces are an action–reaction pair (Newton’s third law), so they are equal in magnitude and opposite in direction even though the currents are different.
Why the other options are incorrect
Option (1) A and B will repel each other with the same force — Incorrect. Parallel wires repel only when their currents are in opposite directions.
Option (3) A and B will attract each other with unequal forces. — Incorrect. The product \( I_1I_2 \) is the same for both wires, so the forces are equal.
Option (4) The magnetic field at mid point between the conducting wires is zero — Incorrect. At the midpoint the two fields are opposite in direction, but the field of the 20I wire is 20 times stronger; they would cancel only for equal currents.
NCERT (2026-27):
Force Between Two Parallel Currents, the Ampere – “… It is of course possible to compute the force on ‘a’ due to ‘b’. From considerations similar to above we can find the force \( \mathbf{F}_{ab} \), on a segment of length \( L \) of ‘a’ due to the current in ‘b’. It is equal in magnitude to \( F_{ba} \), and directed towards ‘b’. Thus,
\( \displaystyle \mathbf{F}_{ba} = -\mathbf{F}_{ab} \qquad (4.18) \)
Note that this is consistent with Newton’s third Law.”
Force Between Two Parallel Currents, the Ampere – “… We have seen from above that currents flowing in the same direction attract each other. One can show that oppositely directed currents repel each other.”