# Magnitude and Direction of Net Force on Loop

A long straight wire carries a current of 31 A to the right. Next to the wire is a square loop with sides 1.0 m in length, as shown in the figure below. The loop carries a current of 2.7 A in the direction indicated. Calculate the magnitude and direction of the net force acting on the loop.

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#### Solution Preview

Okay; so we will start you off. What you are looking at is the application of the Biot-Savart Law, first using the magnetic field of the wire on each section of the loop. That's important. You have to evaluate each section of the loop separately, because the magnetic field from the wire varies with the distance from the wire. I'm adding some enhancements to your drawing. (See diagram.) And please note that your stated information and the information in your drawing do not agree. When you solve this you will have to use whichever numbers are correct.

A long straight wire carries a current of 31 A to the right. Next to the wire is a square loop with sides 1.0 m in length, as shown in the figure below. The loop carries a ...

#### Solution Summary

This solution provides detailed explanation and formula to help the student understand the calculations that need to be done.

Expression for the magnitude and direction of a magnetic field

Please show all the work.

Problem #1: A closed section of a wire in the shape shown in bold in the figure (attached) carries a uniform current I counterclockwise. This section of wire lies completely in the plane of the paper.

The figure consists of three-quarters of a circle of radius R and two straight lines, both of length R. Determine an expression for the magnitude and direction of the magnetic field at the point P (small circle) indicated in the figure.

Your final answer should be in terms of just mu0, I and R.

Problem #2: Three long wires carry currents I1, I2 and I3 with I1 coming perpendicularly out of the page through the point (-a,0), I2 going perpendicularly into the page through the point (0,0), and I3 coming perpendicularly out of the page through the point (+a,0). A fourth long wire carries a current I and passes perpendicularly through the page at the point (+a,+b). If I2 = 50 A, a = 3 m and b = 4 m, determine I1 and I3 so that the total magnetostatic force on I due to I1, I2 and I3 is zero.

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