## Illustration 28.1: Fields from Wires and Loops

The magnetic field around a long, straight wire carrying current out of the computer screen points in a direction that circles the wire (position is given in meters and magnetic field strength is given in tesla). You may want to use a right-hand rule to determine the field direction. If you point the thumb of your right hand out of the computer screen (as if it pointed in the direction of the current) and close your fingers in a fist, then your fingers will point in the direction of the magnetic field around the wire. Instead of one wire, add four wires (again the current in these wires is coming out of the screen). Notice that the vectors from each wire add up. Double-click inside the animation to draw a field line.

What would you expect the direction of the field and the field lines to look like for many wires all lined up in a horizontal row? Sketch your prediction first. Once you have your prediction, try it by pushing the "plate" button. Explain why the field lines look like they do.

For the plate, you should have predicted that the fields from the individual wires that point in the y direction should all cancel. This leaves just a field in the x direction. Since the currents in the wires are all out of the screen, the field points to the left above the plate and points to the right below the plate.

Now, let's put a loop perpendicular to the page. In this representation you are looking at the edge of a loop of wire: The wire goes into the screen, circles around, and comes back out. The blue and red dots simply represent a slice of the wire, with red indicating current coming out and blue indicating current going in. For this case, describe how the current travels (Does the current flow into the screen at the top or the bottom of the loop?). The field points to the right along the center axis of the loop and diverges out from there. Adjust the size of the loop by click-dragging either the red or blue dot. Notice that the region near the center of the loop becomes more and more uniform as the loop gets bigger and bigger.

If you place many loops side by side, what do you expect? Try it by pushing the "solenoid" button. What are the similarities and differences between the field inside a solenoid and the field above a plate? Again the magnetic fields in the y direction all cancel, leaving the magnetic field in the x direction. Given that there is no current enclosed for an Amperian path in the plane with sides outside of the solenoid, the magnetic field is zero there. Inside the solenoid, however, the magnetic field is rather uniform and points to the right.

In order to use Ampere's law, you will need to have a sense of the direction of magnetic fields from a wire or group of wires and then build Amperian loops to match the symmetry of the fields.

Illustration authored by Anne J. Cox.
Script authored by Mario Belloni and Wolfgang Christian and modified by Anne J. Cox.