Question

A square loop, carrying a steady current $I$, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$, at a distance d from the conductor as shown in figure. The loop will experience

• A. a net attractive force towards the conductor
• B. a net repulsive force away from the conductor
• C. a net torque acting upward perpendicular to the horizontal plane
• D. a net torque acting downward normal to the horizontal plane

Answer 1

Answer: (A)

$\vec{ F _{2}}=-\vec{ F }_{4}$
$\vec{ F _{1}}=\frac{\mu_{0} \,I _{1}\, I _{2} \,\ell}{2 \pi d } $
$\vec{ F _{3}}=\frac{\mu_{0}\, I _{1} \,I _{2} \,\ell}{2 \pi( d +\ell)}$
$\vec{ F }_{1}> F _{3}$
So wire attract loop.