Force Between Parallel Currents

Each wire sits in the magnetic field produced by the other, so the force per unit length is $\frac{F}{L}=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$. The direction follows from $\vec{F}=I\vec{L}\times \vec{B}$: parallel currents in the same direction attract, while antiparallel currents repel. Substituting $I_1=5\text{A}$, $I_2=10\text{A}$ and $d=0.04\text{m}$ gives $\frac{F}{L}=\frac{(4\pi \times 10^{-7})(5)(10)}{2\pi (0.04)}=\frac{10^{-5}}{0.04}=2.5\times 10^{-4}{\text{N m}}^{-1}$, and since the currents are codirectional the force is attractive. The repulsive options misidentify the direction for same-direction currents. The value $5.0\times 10^{-4}{\text{N m}}^{-1}$ wrongly halves the separation. The value $1.25\times 10^{-4}{\text{N m}}^{-1}$ doubles the separation. This relation is the very definition NCERT uses for the ampere. A sign check confirms attraction, matching the rule that like currents pull together. This mutual attraction also explains a practical hazard: heavy parallel busbars carrying large currents in the same direction in power stations are physically pulled toward each other and must be braced mechanically. The very definition of the ampere historically rested on this effect, fixing the current that produces a force of $2\times 10^{-7}{\text{N m}}^{-1}$ between wires one metre apart, which ties this microscopic interaction directly to the base unit of electric current. Reversing one of the two currents would flip the sign of the cross product and turn the attraction into an equal repulsion of identical magnitude.