# Current Carrying Wire Loop near Current Carrying Long Wire

A rectangular wire loop of (width $a$ and height $b$) carrying clockwise current $I_1$ is a distance $d$ below a horizontal infinitely long wire carrying a current $I_2$ to the right. What is the force on the wire loop?

I am not sure what equations I have to use here, it's been quite awhile. I know the magnetic field infinite wire is something like $\frac{\mu_0}{2\pi} \frac{I_2}{r}$ And F=v x B. For the horizontal segment of the loop nearest the wire, does $v=\frac{I_1 a}{e}$? Is that right? does F = $\frac{\mu_0}{2\pi} \frac{I_2 I_1 a}{d e} - \frac{\mu_0}{2\pi} \frac{I_2 I_1 a}{(d+b)e} = \frac{\mu_0}{2\pi e}I_2 I_1 a (\frac{b}{d(d+b)})$ towards the wire. Is that the right answer?

• Check the units on $\vec{F} = \vec{v} \times \vec{B}$ you should be able to find the error and correct it. – Brian Moths Sep 30 '13 at 3:22
• Could you be more explicit? I think I should have /rho instead of e. Is that what you are referring to? – walczyk Oct 2 '13 at 4:00
• I was saying that the lorentz force law is $\vec{F} = q \vec{v} \times \vec{B}$ – Brian Moths Oct 2 '13 at 12:59
• Use the force formula for current $d \vec{F} = I \vec{dl} \times \vec{B}$ – M111 Nov 25 '17 at 21:23