## Exploration 28.3: Wire Configurations for a Net Force of Zero

The purple wire and the green wires have fixed currents and fixed positions. You can change the current in the gray wire by using the slider, and you can also drag the gray wire around to new positions. The animation shows the magnetic field vectors as well as the force on the wires. You can also add field lines by double clicking. Restart.

1. What are the directions of the currents in the green and purple wires?

2. Which one carries a larger magnitude of current? Explain.

Keep the current in the gray wire at zero (you can use the "I = 0" button to set the current to zero). Move the gray wire to a spot where the magnetic field is zero. Now increase the current in the gray wire.

1. Why is the force on the gray wire zero?

2. Why isn't the force on the other wires zero?

3. Is the force on the other wires different from the force on those wires before the current was turned on in the gray wire? Explain.

With current in the gray wire, move it to some point where the force is nonzero. The force on the wire is due to the current in the gray wire and the magnetic field it sits in (due to the other wires), F = q v x B = I L x B, where L is the length of the wire and points in the direction of the current in the wire. To determine the direction of the force, then, you use the right-hand rule. Turn the current off in the gray wire.

1. What is the direction of the net magnetic field (make a sketch)?

2. Positive current comes straight out of the computer screen (negative current is into the screen). Therefore, in what direction is I L x B for negative current (indicate this on your sketch)? Try it and verify your answer.

3. With a negative current, where does the gray wire need to be located so that the force on the purple wire is zero? So that the force on the green wire is zero? Explain.

4. If you change the current, how does your answer to (h) change? Explain.

Try a different configuration.

1. Where will the force be zero on the gray wire when it has a current flowing in it?

2. If the gray current has a current of about -1 A, where do you have to put it in order to get the force on the green wire to be zero? Where do you have to put it in order to get the force on the purple wire to be zero? Where do you have to put it in order to get the force on the yellow wire to be zero? Explain.

Exploration authored by Anne J. Cox.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.