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Two long parallel wires separated by distance $d$ carry currents $I_1$ and $I_2$ in the SAME direction. The force per unit length between them is
Arepulsive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
Battractive, $\dfrac{\mu_0 I_1 I_2}{4\pi d^2}$
Cattractive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
Dzero
Answer & Solution
Correct answer: C. attractive, $\dfrac{\mu_0 I_1 I_2}{2\pi d}$
1. Wire 1 produces a magnetic field at wire 2's location: $B_1 = \mu_0 I_1/(2\pi d)$, direction given by right-hand rule.
2. Force on a length $L$ of wire 2: $F = I_2 L B_1 = \mu_0 I_1 I_2 L /(2\pi d)$.
3. Force per unit length: $F/L = \mu_0 I_1 I_2 /(2\pi d)$.
4. DIRECTION: parallel (same-direction) currents ATTRACT; antiparallel currents REPEL. Quick check via right-hand rule: B from wire 1 at wire 2 points one way; force $\vec{I_2 L}\times\vec{B}$ points toward wire 1.
5. This is THE DEFINITION of the ampere: 1 A is the current that produces $2\times 10^{-7}\,\text{N/m}$ between parallel wires 1 m apart.
6. Option B has wrong direction (repulsive). Option C has wrong distance dependence. Option D forgets the interaction exists.
_Source: NCERT Class 12 Physics Part 1, Ch 4, §4.7 (Force Between Two Parallel Currents — definition of ampere), p. 19–20._
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