PC1143 Physics III
Current Balance
1
Objectives
• Investigate how the magnetic force on a current carrying wire is related to current,
length of wire, magnetic field strength, and angle between current and magnetic field.
• Determine experimentally the magnetic field strength of the magnets used.
2
Equipment List
• Current balance apparatus
• DC power supply
• Electronic balance
3
Theory
~ it experiences
If a charged particle moves with velocity ~v through a uniform magnetic field B,
a magnetic force given by
~
F~ = q~v × B
(1)
where q is the amount of charge on the particle. If the angle between the particle’s velocity and
the direction of the magnetic field is θ, the magnitude of the magnetic force can be rewritten
as
F = qvB sin θ .
(2)
The direction of the magnetic force may then be found with the familiar right-hand rule.
~ and is identically
Notice that the magnitude of the magnetic force is a maximum when ~v ⊥ B
~
zero when ~v k B.
Consider a straight segment of a wire carrying a current I within a uniform magnetic field
~ The magnetic force on each charged particle is then given by
B.
~,
F~ = q~vd × B
(3)
where ~vd is the drift velocity of the charged particles. The volume of the wire that exists
within the magnetic field is A`, where A is the wire’s cross-sectional area and ` is the length
of the wire that is embedded within the magnetic field. If we define n to be the number of
charged particles per unit volume, the total amount of charges within that segment of wire
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Current Balance
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will be given by nA` at any instant. The magnetic force acting on the wire can then be
expressed as
~ .
F~ = nA`q ~vd × B
(4)
Since the current flowing in a conductor is given as I = nqvd A, the magnetic force acting on
a current-carrying wire becomes
~,
F~ = I ~` × B
(5)
where ~` is the vector length of wire that points in the direction of the current I. Note that the
direction of the current is defined as the direction in which positively charged objects move.
~ are mutually perpendicular then we have
The magnetic force will be a maximum if ~` and B
F = I`B .
(6)
Figure 1: Equipment setup.
Our experimental setup is schematically shown in Figure 1 and is described as follows. A
permanent magnet assembly, comprised of six removable horseshoe magnets, is placed on a
balance and the balance is then zeroed. A variable current source is connected to the current
balance assembly, which has at one end a removable wire loop PC circuit board. This wire
loop is then placed into the permanent magnet assembly so the wire loop is perpendicular to
the magnetic field but is not touching the magnets. Then, when a current flows through the
wire loop, a magnetic force is created. Since the wire loop is stationary the magnetic force acts
on the permanent magnet assembly causing its weight to either increase or decrease depending
on the direction of the current and the orientation of the magnetic field. The change in the
magnet assembly’s weight is due to the magnetic force given by (5).
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Current Balance
4
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Laboratory Work
Part A: Force versus Current
In this part of the experiment, the length of the wire, the strength of the magnetic field,
and the angle between wire and magnetic field will be kept constant. We will investigate the
magnetic force acting on a current-carrying wire as a function of the current passing through
it.
A-1. Mount the main unit on a lab stand as shown in Figure 1.
A-2. Select the current loop labeled SF42 and plug it into the ends of the arms of the main
unit with the conductive foil facing down.
A-3. Connect the power supply as shown in Figure 2.
Figure 2: Connecting with the power supply.
A-4. Place the magnet assembly labeled A on the electronic balance. Position the lab stand
so the horizontal portion of the conductive foil on the current loop passes through the
pole region of the magnets. The current loop should NOT touch the magnets.
A-5. Switch on the electronic balance. With no current flowing, zero the balance reading by
pressing the “TARE” button once.
A-6. Switch on the power supply, reverse the leads connected to the arms of the main unit if
the balance reading is negative.
A-7. Set the current to 0.5 A and record the reading on the electronic balance as “Force” in
Data Table 1.
A-8. Increase the current in 0.5 A increments to a maximum of 5.0 A, each time recording the
new “Force” value in Data Table 1.
A-9. Reduce the current to 0.0 A. Swing the arm of the main unit up, to raise the current
loop out from the pole region of magnets. Pull the current loop gently from the arms
of the main unit. Replace it with the current loop labeled SF40. Carefully lower the
arm to reposition the current loop in the pole region of the magnets. Repeat steps A-4
through A-8.
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Current Balance
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Part B: Force versus Length of Wire
In this part of the experiment, the current, the strength of the magnetic field, and the angle
between wire and magnetic field will be kept constant. The variation of the magnetic force
acting on a current-carrying wire with the length of the wire will be investigated.
B-1. Set up the apparatus as in steps A-1 through A-3 in part A.
B-2. Place the magnet assembly labeled A on the electronic balance. Position the lab stand
so the horizontal portion of the conductive foil on the current loop passes through the
pole region of the magnets. The current loop should NOT touch the magnets.
B-3. Switch on the electronic balance. With no current flowing, zero the balance reading
by pressing the “TARE” button once. Switch on the power supply, reverse the leads
connected to the arms of the main unit if the balance reading is negative.
B-4. Now turn the power supply on and set the current to 2.0 A. Record the reading on the
electronic balance as “Force” in Data Table 2.
B-5. Reduce the current to 0.0 A. Swing the arm of the main unit up, to raise the current
loop out from the pole region of magnets. Pull the current loop gently from the arms
of the main unit. Replace it with another current loop. Carefully lower the arm to
reposition the current loop in the pole region of the magnets.
B-6. Repeat steps B-1 through B-5 for the rest of the current loops.
Part C: Force versus Magnetic Field
In this part of the experiment, we will investigate the dependence of the magnetic force on
the strength of the magnetic field with a fixed length of the wire.
C-1. Set up the apparatus as in steps A-1 through A-3 in part A with the shortest current
loop (SF40).
C-2. Mount a single magnet in the center of the magnet holder.
C-3. Place the magnet assembly labeled A on the electronic balance. Position the lab stand
so the horizontal portion of the conductive foil on the current loop passes through the
pole region of the magnets. The current loop should NOT touch the magnets.
C-4. Switch on the electronic balance. With no current flowing, zero the balance reading
by pressing the “TARE” button once. Switch on the power supply, reverse the leads
connected to the arms of the main unit if the balance reading is negative.
C-5. Now turn the power supply on and set the current to 2.0 A. Record the reading on the
electronic balance as “Force” in Data Table 3.
C-6. Add additional magnets, one at a time till all six magnets are used. Make sure the same
coloured poles are all on the same side of the magnet assembly and are centered at the
center of the magnet holder. Each time you add a magnet, repeat steps C-3 through
C-5.
C-7. Repeat steps C-1 through C-6 with the longest current loop (SF42).
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Current Balance
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Part D: Force versus Angle
In this part of the experiment, we will investigate the dependence of the magnetic force on
the angle between the wire and the magnetic field.
D-1. Mount the main unit on a lab stand as shown in Figure 3.
Figure 3: Equipment setup with goniometer.
D-2. Pull the current loop gently from the arms of the main unit. Replace it with the
goniometer assembly.
D-3. Connect the power supply as shown in Figure 2.
D-4. Place the magnet assembly B on the electronic balance. Carefully lower the arm to
reposition the current coil of the goniometer in the pole region of the magnets.
D-5. Set the dial on the unit to 0◦ .
D-6. Switch on the electronic balance. With no current flowing, zero the balance reading by
pressing the “TARE” button once.
D-7. Align the magnetic assembly B so that the magnetic field is parallel with the horizontal
(bottom most) wires of the coil of the goniometer assembly.
Note: You could apply some current to the loop and adjust the magnet assembly B or
the goniometer assembly until the reading on the electronic balance is zero.
D-8. Now set the current to 1.0 A. Record the reading on the electronic balance as “Force”
in Data Table 4.
D-9. Increase the angle clockwise in 10◦ increments up to 90◦ , and then counterclockwise in
−10◦ increments to −90◦ . Repeat the “Force” measurement at each angle.
Last updated: Saturday 14th February, 2009 11:22pm (KHCM)
Physics Level 1 Laboratory
c Department of Physics
National University of Singapore