Force of a Magnetic Field on a Current-Carrying Wire
Introduction
A current-carrying wire in a magnetic field 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 Newtons
can be described mathematically by the vector cross-product:
F i B
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:
F  i B sin 
and the 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
SF
SF
SF
SF
SF
SF
40
37
39
38
41
42
Length
1.0
2.0
3.0
4.0
6.0
8.0
cm
cm
cm
cm
cm
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 F  i B sin  (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 Apparatus
Fig. 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 height and 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 DMM to 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
vertical force 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 to 7 until 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?