Physics Electrical Question

Consider a rectangular loop of wire placed in the same plane as a straight wire. a current of 2A runs through the rectangular loop. The dimensions of the loop are 1 m x 0.05 m. A current of 8A runs through the wire. The wire is parallel to the 1m side of the loop and the distance from the wire to the nearest 1m side of the loop is 0.05 m. Does the loop experience a net force? If so, determine the magnitude and the direction of the net force on the loop.If not, explain why not. Show your work and explain your reasoning.


The answer is YES the loop experience a net force on it. Explications follows.

The magnetic induction generated by wire at a distance r from it is

$B =\mu*I/2/r$,

where $mu$ is the absolute magnetic permeability of the air , $mu =4*\pi*10^-7$ H/m

The force on a side of the loop is

$F = B*I*l$ where l is the length of the side and I the current through that side.

The magnetic force on the sides perpendicular to the wire cancel each other and it remains only the magnetic forces applied to the sides parallel to the wire which are opposite.

In the figure the dimension of the loop is 1 meter x 5 cm and in the text the dimension of the loop is 1 m x 50 cm. I am taking the dimensions of the loop from the figure not from the text!!!

$F = (B1-B2)*I*l = \mu*I_{wire}/2*(1/r1 -1/r2)*I_{loop}*l =$

$=4 \pi*10^{-7}*8(1/0.05 -1/0.1)*2*1 =2*10^{-4}$ N