Derive an expression for the force per unit length between two infinitely long straight parallel current-carrying wires. Hence,define one ampere $(A)$.

(N/A) Consider two infinitely long,straight,parallel wires separated by a distance $d$,carrying currents $I_a$ and $I_b$ respectively.
The magnetic field $B_a$ produced by wire $a$ at the location of wire $b$ is given by Ampere's circuital law: $B_a = \frac{\mu_0 I_a}{2 \pi d}$.
The magnetic force $F$ on a length $L$ of wire $b$ due to this magnetic field is $F = I_b L B_a \sin(90^\circ) = I_b L \left( \frac{\mu_0 I_a}{2 \pi d} \right)$.
Thus,the force per unit length $f = \frac{F}{L}$ is given by: $f = \frac{\mu_0 I_a I_b}{2 \pi d}$.
Definition of one ampere $(A)$: One ampere is that constant current which,if maintained in each of two infinitely long,straight,parallel conductors of negligible cross-section placed $1 \ m$ apart in a vacuum,would produce on each of these conductors a force equal to $2 \times 10^{-7} \ N$ per meter of length.