Force of a
Magnetic Field on a Current-Carrying Wire
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 (L), the strength and direction of the magnetic field (B),
and the angle between the field and the wire (Θ). The force can be described
mathematically by the vector cross-product:
F = I L X B
Or
in scalar terms:
F = I L B SinΘ
When current is in amperes,
length in meters, and magnetic field in teslas, the force
is
in newtons.
The
direction of the force is perpendicular to both the current and the magnetic
field, and is predicted by the right-hand cross-product rule.
For a more detailed discussion of the
above material, read the following pages in your textbook (for Physics 212,
pages 736 to 738 and 750 to 751.)
Equipment
O’Haus Four-Beam
Balance
Lab Stand
(V-Shaped Base and Attached 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
*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
F = I L B (for Θ = 90 degrees)
with two sets of measurements:
1. Holding
L and B constant, vary the current, 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
- Preliminary
Set-Up
1. Place the magnet assembly on the tray of the
four-beam balance.
2. Mount
the main unit of the current balance on the vertical rod supported by
the lab
stand.
3. Plug
current loop board SF 39 (3.0cm) into the main unit. 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.
4. With the power supply off, attach two leads
to the +
and - terminals of the
DC (left) side of the power
supply. Connect the + lead to the 10A terminal of the
multimeter. Connect the COM
terminal of the multimeter to the top of the current
balance. Connect the -
power supply lead to the other terminal of the current balance.
5. Set the multimeter on 20m/10A and on DC, and
turn it on.
6. In the power supply, turn the voltage and
current dials counterclockwise to the
zero position.
- Data
Collection for Force versus Current
1.Record the
weight of the magnet (when no current is passing through the wire.)
2. Turn on the power supply, (V and I should
both read zero.)
3. Turn the voltage dial about 1/4 turn
clockwise.
4. Slowly turn the current dial until the current is one
amp. Notice that the a vertical
force has changed
the reading of the balance. Take a new balance reading. (The
change in
“weight” is the force that the magnetic field is exerting on the wire.)
- Repeat step 4 for two, three, four, and
five amps.
C.
Data Collection for Force versus Wire Length
1. Reduce the current to zero. Replace the
current loop with the 1.0 cm current
loop.
- With
current at zero, record the weight.
- Raise
the current to 5 amps and record the new current balance reading.
- Repeat
steps 1 to 3 with each of the six current loops.
D. Magnetic Field Strength
Use the Gaussmeter on the instructor’s desk
to measure the magnetic field
of your magnet assembly.
Computations
- Variation
of Force with Current
- For
each current setting, find the force, which is the difference between
the magnet assembly weight and the
balance reading. Convert grams to kilo-
grams and multiply by g to
obtain the force in newtons.
- Calculate
the theoretical value of the force for each current setting using
F = I L B
- Compare
each measured force with the corresponding theoretical value
and calculate each percent
difference.
- Plot
the measured force versus current and obtain a best-fit straight
line.
Compare the value of its slope
with the product of L and B.
- Variation
of Force with Length
- Using
the force versus length data repeat steps 1 to 3 of the previous
computations.
- Plot measured
force versus length and obtain a best-fit straight line. Compare
its slope with the product of I
and B.
