21.3

Magnetic Field Produced by a Current Loop

Student Notes

You can use this simulation to examine the magnetic field created by the current in a wire loop. The loop is in the x-z plane, centered on the origin, with a radius of 0.6 m initially. The displayed field is in the x-y plane.
Here are some things to consider. How does the magnetic field depend on the magnitude of the current? What happens to the magnetic field if the direction of the current is reversed? Using the right-hand rule relating current and magnetic field, you should be able to predict the direction of the magnetic field created by the current in the loop. Try the right-hand rule for yourself, and make sure you get the same result for the direction of the magnetic field that the simulation does. Where is the magnetic field strongest? Is it at the very center of the loop, or near the edge of the loop? How uniform is the field inside the loop? Is the magnitude of the field significantly different at the center of the loop from what it is near the edge of the loop?

Self-test

Halliday version: The center of the loop is at X = 0, Y = 0. The magnetic field at this point can be calculated using the equation B = m oI / 2r, where r is the radius of the loop. It is more challenging to determine the field at other places, but it can be done using the Biot-Savart Law. Look up the Biot-Savart Law in your textbook, calculate the magnitude of the magnetic field at X = 0, Y = 1 m, and see if your answer agrees with that given by the simulation at that point. Doubling the current doubles the magnitude of the magnetic field. Does doubling the current affect the shape of the magnetic field in any way? What is the shape of the magnetic field determined by?
Cutnell version: The center of the loop is at X = 0, Y = 0. The magnetic field at this point can be calculated using the equation B = m oI / 2r, where r is the radius of the loop. Calculate the field at the center of the loop and compare it to the field determined by the simulation. Doubling the current doubles the magnitude of the magnetic field. Does doubling the current affect the shape of the magnetic field in any way? What is the shape of the magnetic field determined by?

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