Question

A long straight conductor carrying $I_1$ is placed in the plane of ribbon at a distance a from the near edge of a ribbon of width b, which carries $I_2$ parallel to the wire. Find the force of attraction per unit length between the two.

Answer 1

dF (force of attraction) due to strip of thickness dx at a distance $xdF=\frac{{\mu }_{0}i{I}_1}{2\pi x}\left(\frac{I_{2}dx}{b}\right)$
$F=\frac{{\mu }_0{I}_1{I}_2}{2\pi b}{\int }_a^{a+b}\frac{dx}{x}=\frac{{\mu }_0{I}_1{I}_2}{2\pi b}In\left(\frac{a+b}{b}\right)$