Chapter 28 Problem 24

Problem

Current loop and wire

A triangular loop of side length a carries a current $I$. If this loop is placed a distance $d$ away from a very long straight wire carrying a current $I^{\prime }$,determine the force on the loop.

Solution

The current in the parallel branch flows in the same direction as the long straight wire, so the force is attractive with magnitude:

$F_{1}={\frac {\mu _{0}II^{\prime }}{2\pi d}}a$

By symmetry the magnetic force for the other two segments will be equal.

$F_{2}=\int _{0}^{a/2}{\frac {\mu _{0}II^{\prime }}{2\pi d}}a$