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force on rectangular loop

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The top side of a 7cm by 4 cm rectangular loop of wire is 2 cm from a long straight wire.

The long wire is in the same plane as the rectangle, and they have the currents shown. Find

the force (magnitude & direction) on the rectangular loop. How do you solve this?
asked Apr 21, 2014 in Others by anonymous

1 Answer

0 votes
First we need to look at the magnetic field produced by the long straight wire which we know from Ampere's Law:

\( B= \frac{\mu_0 I}{2 \pi r} \)

In the plane of the rectangular loop, the direction of the magnetic field will be either into the page or out of the page depending on the direction of current in the wire (use the right hand rule to determine).

This field will produce a force on each side of the current-carrying loop:

\( F= I L \times B \)

The force on the two sides perpendicular to the wire will be equal and opposite. The force on the parallel sides will be in opposite directions, but stronger on the side closer to the wire. The difference in these two forces will determine the magnitude and direction of the overall force (either towards or away from the wire...depending on the current in the wire and loop).
answered Apr 24, 2014 by jcf1559 (2,140 points)
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