Force of a Magnetic Field on a Current-Carrying Wire

Introduction

A current-carrying wire in a magneticfield experiences a force. The magnitude and direction of this force depend on four variables: the magnitude and direction of the current (i), the length of the wire (), the strength and direction of the magnetic flux density (B), and the angle between the field and the wire (). The force in Newtonscan be described mathematically by the vector cross-product:

where the current is in Amperes, the length of the wire in meters, and the magnetic flux density (“strength of the field”) is in Teslas. The magnitude of the force is then:

andthe direction of the force is perpendicular to both the current and the magnetic flux density, and is predicted by the right-hand rule.

For a more detailed discussion of the above material see your textbook.

Equipment

O’Haus Four-Beam Balance

Large table clamp with short rod

Pasco Current Balance (SF-8607), consisting of

  1. Main Unit
  2. Magnet Assembly, with Six Magnets
  3. Six Different Current Loop Boards*

Kelvin 200LE Multimeter

Pasco Low Voltage AC/DC Power Supply (SF-9584A)

*For each of the current loop boards, the length of the straight-line segment that will lie in the magnetic field is as follows:

Current Loop Length

SF 40 1.0 cm

SF 37 2.0 cm

SF 39 3.0 cm

SF 38 4.0 cm

SF 41 6.0 cm

SF 42 8.0 cm

(These lengths are the distances between the centers of the vertical wires bringing current into and out of the segment.)

Objective

To verify the relation (for = 90o) for the following cases:

  1. Holding and B constant, vary the current i, and measure how the force on the wire varies with current.
  2. Holding i and B constant, vary the length (), and measure how the force on the wire varies with length.

Procedure

Fig. 1 Magnetic Balance ApparatusFig. 2 Low Voltage Power supply and DMM

Assemble the apparatus as shown in Figs. 1 and 2.

  1. Plug a current loop board into the main unit. (It is suggested you choose one of the longer current loops here.) Adjust its heightand position so that the straight wire segment is centered between the (white and red) magnetic poles. Make sure the current loop board does not touch the magnetic poles.
  2. Attach two leads to the + and - terminals of the DC (left) side of the power supply as shown in Fig. 2. Connect the + lead to the 10A terminal of the DMM. Connect the COM terminal of the DMM to the top of the current balance. Connect the - power supply lead to the other terminal of the current balance.
  3. Set the DMMto 20m/10A range and on DC, and turn it on.
  4. Be sure to turn the current control and voltage control to zero (full counterclockwise).
  5. Be sure to have your instructor check your wiring and apparatus setup before proceeding.

Collecting Data

You will need to determine the “change in weight” of the magnet assembly due to the effect of the magnetic force on it. You should also include a sketch of the assembly in your report and label the North and South pole of the assembly.

Before collecting data, be sure that the balance is properly “zeroed.”

Next determine mass of the magnet assembly (with zero current in the wire assembly).

Follow the procedure below to collect your data. DO NOT exceed the 5 amp rating of the magnetic loop apparatus!

  1. Turn on the power supply, (V and I should both read zero.)
  2. Turn the voltage dial about 1/4 turn clockwise.
  3. Slowly turn the current dial until the current is one amp. Notice that the verticalforce has changed the reading of the balance. Take a new balance reading. (From the change in “weight” calculate the force exerted on the wire by the magnetic field.)
  4. Repeat step 4 for two, three, four, and five amps.
  5. Reduce the current to zero. Replace the current loop with another one of the current loops.
  6. With current at zero, check the weight of the magnets. Record the new value if it changes.
  7. Increase the current to about 4 amps and record the new current balance reading.
  8. Repeat steps 5 to7until each of the current loops have been used to measure the magnetic force exerted by the current you chose in step 7. Be careful to obtain the same current for each loop so you can determine the dependence of magnetic force on length.
  9. Use the Gaussmeter (Fig. 3) to measure the magnetic flux density of your magnet assembly at its center.
  10. Look up the manufacturer’s claim for accuracy of the Gaussmeter in the instrument’s manual and record this information.

Fig. 3 Gaussmeter

Analysis and Report

  1. On your sketch of the apparatus determine using the right hand rule whether the red or white pole is north. Label the diagram as such.
  2. Plot the magnetic force vs. current for the data you collected with the first current loop. Obtain a linear trendline and equation for your graph. Does the slope of the graph equal the product of magnetic flux density and loop length?
  3. Using the data collected for the several different current loops, plot a graph of magnetic force vs. length. Obtain a linear trendline and equation for your graph. Is the slope of the line equal to product of current and magnetic flux density?
  4. Calculate the value of B from the slope of the trendline in each of the cases above. Compare these values with the value of B determined directly with the Gaussmeter. Are these computed values of B within the range of uncertainty of the Gaussmeter.
  5. What are your sources of experimental error?