General Physics Experiment Handout
Electromagnetic Force and Electromagnetic Induction
Purpose
In this experiment, the correlations between electromagnetic forces and currents
passing through a conducting wire and solenoid were observed. The purposes of this
experiment were as follows:
1. Observe the correlations between the magnetic force and the current in a currentcarrying wire placed in a magnetic field.
2. Observe the correlations between the strength of the magnetic field in the solenoid
and the current in the solenoid wire when the current passed through a solenoid is
constant. In addition, verify Faraday’s law of induction by observing the
electromagnetic induction between two wire loops.
Principles
The primary instruments used in electromagnetic force experiments are a current
balance and a solenoid. A current balance is used to measure the magnetic force of a
current-carrying wire, and a solenoid is used to create a uniform magnetic field that can
be controlled by the current level. The principles of these two instruments are explained
below.
A.
Magnetic field B inside a solenoid
A solenoid is produced by winding a conducting wire, such as a magnet wire,
uniformly on a hollow insulated coil. In ideal conditions, a uniform and directional
magnetic field is generated inside the solenoid when the conducting wire is charged
with a current I1. Additionally, the magnetic field B can be measured using
Ampère's law:
(1)
B = µ nI
0
1
(refer to the General Physics textbook) where µ is the magnetic constant in a vacuum
−7
( µ 0 = 4π × 10 T ⋅ m/A ), and n is the number of turns per unit length.
0
B. Current balance
Figure 1 shows a current balance structure. The main structure of this current
balance consists of a rectangular printed circuit board (PCB). Two pieces of metal at
the center of the PCB are used as the balance fulcrum. Weights of m mass are placed on
both sides of the PCB. Opposite the PCB is a U-shaped conducting wire. A current is
introduced through the balance fulcrum from the “supports.”
When the U wire of the current balance is placed in a magnetic field B, the wire
is influenced by a magnetic force F that tilts the balance if a current I2 is inputted into
the wire. This magnetic force can be measured using the formula for a magnetic force
on a long straight conducting wire. This formula is
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General Physics Experiment Handout
r
r r
F = I2L × B
(2)
r
L
is a vector parallel to I2, and its value equals the length of the wire.
A counterbalance of m mass can be placed on the other side of the current balance to
maintain equilibrium because of the gravitational force of the weights. This equilibrium can be
used to measure the magnetic force on the wire.
Scale
U wires
Supports
Platform for
weights
Figure 1. Current balance
The principle used in electromagnetic induction experiments is known as Faraday’s law.
If the magnetic flux through a surface with a wire loop boundary varies over time, the wire
loop acquires an electromotive force (EMF). This EMF is directly proportional to the time
derivative of the magnetic flux and can be determined using
ε =−
∂Φ B
∂t
(3)
The minus sign in the formula is the result of Lenz’s law, which states that an induced current
(or an induced EMF) produces an induced magnetic field along the direction of the current (or
the EMF) to oppose the change in magnetic flux caused by the EMF.
Figure 2 shows the experimental instruments. The voltage produced by a function
generator is a pulsating signal of a fixed frequency generated by the function generator. Using
a T-connector, a fixed-frequency pulsating signal is simultaneously inputted into Wire Loop 1
and the CH 1 input of an oscilloscope. This signal induces a fixed-frequency pulsating current.
The frequency of the voltage (or current) is determined using CH 1, and the magnetic flux
through the surface of Wire Loop 1 changes accordingly.
If placed within the magnetic fields produced by Wire Loop 1, Wire Loop 2 creates an
EMF because of the change in magnetic flux through the surface of Wire Loop 1. This EMF
can be observed using an oscilloscope by connecting Wire Loop 2 to CH 2 of the
oscilloscope.
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General Physics Experiment Handout
圖二-Figure 2, 信號產生器-Function Generator, 第一線圈-Wire Loop 1, 第二線圈Wire Loop 2, 示波器- Oscilloscope
Experimental instruments
1. Current balance with a base
2. Solenoid
3. Two DC power supply sources (maximum output: 5 V and 3 A)
4. Small weights
5. Four power cables
6. Induction wire loop (white)
Notes
※ To prevent the conducting wires from overheating and damaging the insulation
layer, the input current (DC) of the U wires and the solenoid of the current balance
must not exceed 3 A.
Procedures
A.
Instrument setup
1. Position the current balance on the supports. Adjust the numbers and positions
of rubber bands on the PCB to ensure the PCB remains horizontal.
Subsequently, record the reading on the scale at the base to mark the level
position of the balance.
2. Insert one of the U wires into the solenoid cautiously. Do not contact the
internal structure of the solenoid.
3. Connect the solenoid and the U wire to the left and right output connections of
the DC supply. Typically, the black connector is connected to the negative, and
the red connector is connected to the positive.
※ Switch the power supply off before making connections.
4. Set the DC power supply to “independent mode” (INDEP) to ensure that the left
and right output connections output two sets of the desired current or voltage.
5. Set both connections of the power supply to “constant output current.”
6. Set both the current I2 in the U wire and the I1 in the solenoid to 2 A. Observe
whether the current balance is tilted when a downward force is applied to the U
wire (the end in the solenoid should move downward).
※ If the balance tilts to the opposite side, switch off the output current, and
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General Physics Experiment Handout
reverse the current direction in the solenoid (or the U wire).
Figure 2. Experimental instruments
B. Measuring the correlation between the magnitude of wire currents and the
magnetic forces
1. Set the current I1 in the solenoid to a constant value. (Caution: I1 is advised to
range between 2 and 3 A. To prevent overheating and distortion of the cable
connectors, do not set I1 over 3 A).
2. Place small weights of a specific mass at a fixed position on one end of the
current balance (e.g., the area marked “platform for weights” on the PCB).
Adjust the current I2 passing through the balance to restore its equilibrium.
Because the weights apply a gravitational force mg to the balance, the magnetic
force F placed on the wire by I2 can be calculated.
3. Repeat Procedure 2 with at least 5 sets of weights to obtain several correlation
sets between F and I2.
4. Use I2 as the vertical axis and F as the horizontal axis to plot a correlation graph
of the results. Based on this graph, identify the correlations between the current
I2 in the wire and the magnetic force F of a fixed magnetic field.
C. Correlations between magnetic field B and solenoid current I1
1. Set the current I2 in the current balance to a constant value (e.g., I2 = 2 A).
2. Place small weights of a specific mass at a fixed position on one end of the
current balance (e.g., the area marked “platform for weights” on the PCB).
Adjust the input current I1 passing through the solenoid to restore the balance
equilibrium. Use the mass of the weights to calculate the magnetic force F
applied to the wire. Based on Formula 2, the magnetic field B in the solenoid can
be determined.
3. Repeat Procedure 2 with at least 5 sets of weights to obtain several correlation
sets between F and I1.
4. Use I1 as the vertical axis and F as the horizontal axis to plot a correlation graph
of the results. Based on this graph, identify the correlations between the current
I1 and the magnetic field B in the solenoid.
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General Physics Experiment Handout
D. Verification of Faraday’s law
1. The larger white induction wire loop is Wire Loop 1, and the solenoid used in
Experiment C is Wire Loop 2.
2. According to Fig. 2 in the Principles section, connect the function generator to
the oscilloscope’s CH 1 and to Wire Loop 1. Then connect Wire Loop 2 to the
oscilloscope’s CH 2.
3. Generate a 1-kHz sawtooth wave using the function generator.
The peak-to-peak voltage Vp-p of this signal directly influences the
magnitude of the current in the loops and the strength of the magnetic field.
Vp-p is recommended to be set at approximately 10 V.
4. Set the oscilloscope into DUAL mode and simultaneously observe waveforms in CH
1 and CH 2.
Compared to signals from the induction loops, signals generated by the
function generator are more stable. Therefore, using the oscilloscope to
trigger the signal in CH 1 for reference is recommended.
5. Adjust the function generator to generate sine waves and square waves. Record
the waveforms shown in CH 1 and CH 2.
6. Reverse the positive and negative of either loop. Observe and record the changes
shown in CH 2.
7. Change the distance between the two loops. Observe and record the changes
shown in CH 2.
※ Observe whether a phase difference exists between the signals in CH 1 and
CH 2.
※ During the experiment, attempt to explain the effects of input wave changes
using Faraday’s law.
Discussion questions
1.
Is the magnetic field in the solenoid uniform? How can you verify this?
2.
Attempt to calculate the number of turns in the solenoid based on the experimental
results.
3.
The figure below shows the possible directions of a magnetic field produced by the
edge of the solenoid. Does this magnetic field apply force to the U wire and, thus,
influence the results?
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