A straight wire has $n$ mobile, charged particles per unit length, each of charge $q$. Assuming the charges all move with velocity $v$ along the wire, show that the current is $I=n q v$.

Using the Lorentz force law, show that if such a current-carrying wire is placed in a uniform magnetic field of strength $B$ perpendicular to the wire, then the force on the wire, per unit length, is $B I$.

Consider two infinite parallel wires, with separation $L$, carrying (in the same sense of direction) positive currents $I_{1}$ and $I_{2}$, respectively. Find the force per unit length on each wire, determining both its magnitude and direction.