Magnetic Field About Wire

The apparatus is shown below. It consists of a round plexiglass table with a perpendicular aluminum rod through its center. Two contacts for the banana cables are attached at either end. When a large current is run through the rod, the rotation of compasses will show the magnetic force. This demonstration requires a video camera suspended above the apparatus (see picture to the left).

Equipment:

  • Round Plexiglass Table with a Perpendicular Aluminum Rod through its Center
  • 2 Banana Cables
  • Fisher Scientific Power Supply
  • Compasses (2 or 4)
  • Video Camera on Tripod

Demo:

  • Attach the two banana cables to either end of the aluminum rod and to the Fisher Scientific Power Supply.
  • Place the compasses around the aluminum rod on the plexiglass table.
  • Turn on the power supply.
  • Increase the voltage to the maximum setting on the Fisher Scientific Power Supply, and then slowly increase the current on the Fisher Scientific Power Supply. Note to not exceed 10A.

You should see the compasses start to rotate once current is flowing through the aluminum rod. This demonstrates the relationship between magnetic fields and currents, which is summarized with Ampere’s law.

To reverse the current that is traveling through the wire, turn the current and voltage on the Fisher Scientific Power Supply to 0, and turn off the power supply. Switch the two ends of the banana cables that are attached to the power supply. Turn on the Fisher Scientific Power Supply. Increase the voltage, and then the current. The current will now travel in the opposite direction.

Explanation:

Ampere’s law gives a relation between a closed magnetic field loop and the current that is enclosed by the magnetic field loop:

\int B\cdot dl = \mu_o I_{enc}

where B is the magnetic field, dl is the length element of a closed path, \mu_o is the permeability of free space, and I_{enc} is the current that is enclosed by the path of the magnetic field that is being examined. In this demonstration, the closed path is the area surrounding the straight wire. This is shown in Figure 1.

Figure 1: Ampere’s law is shown. A current I is traveling down the wire towards the right. This produces a magnetic field that encloses the wire in a counter-clockwise direction, which is determined by the right hand rule.

This gives a magnetic field with a magnitude B=\frac{\mu_o I_{enc}}{2\pi r}, where r is the radial distance from the wire. The direction of the magnetic field produced by the straight wire is determined by the right hand rule. The current in this demonstration can only travel through the aluminum rod, which magnetic field produced by this current will be counterclockwise if the current travels upward, or clockwise if the current travels downwards.

Notes:

  • Aligning 2 compasses with the longitude allows them to turn 90° in opposite directions when the current goes through the rod.
  • If 4 compasses are used, one of them will not turn.

 

Written by Ryan Dudschus