Question

The magnitude of f of the force between two straight parallel current carrying coductors kept at a distance d apart on air is given by

Answer 1

since two wires are placed "d" distance apart

so the two wires will exert force on each other as magnetic field of one wire will apply force on other wire

So here the magnetic field of first wire at the position of other wire is given by

$B = \frac{\mu_o i_1}{2\pi d}$

here i1 = current in first wire

now since the other wire is placed in this field

so force on the other wire will be

$F = iLB$

$F = i_2*\frac{\mu_o i_1}{2\pi d}* L$

now the force between two wire is given by formula

$F = \frac{\mu_o i_1 i_2 L}{2\pi d}$

here L is the length of wire on which force is applied