5K10.20 Induction Coil with Magnet,
Galvanometer
Abstract
When a magnet is moved through a coil of wire, a current is induced in the coil. A galvanometer connected
to the coil measures this induced current. The strength of the induced current is altered by varying the relative
speed between the magnet and the coil, and the polarity of the reading on the galvanometer reverses when the
motion of the magnet reverses direction. A current is also induced in the coil if the magnet is held stationary and
the coil is rotated about its handle.
Picture
Setup
Setup is 0 minutes.
Safety Concerns
None.
Equipment
• Induction Coil
• Galvanometer
• Connecting Leads
• Overhead Projector
• Cylindrical Magnet
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Procedure
Check to see if the galvanometer is calibrated. It should initially read zero. If the galvanometer is not
calibrated, the white plastic screw can be turned clockwise or counterclockwise until the needle points at zero.
Place the galvanometer on the overhead projector. Insert the magnet into the coil and watch the reading on the
galvanometer. Withdraw the magnet from the loop to produce a reading of the opposite polarity. Hold the magnet
still to show that when there is no motion between the magnet and the coil the galvanometer reads zero. Similarly,
the magnet can be held stationary while the coil moves closer and further from it. If the poles of the magnet are
reversed (i.e. the magnet is flipped), the reading on the galvanometer reverses polarity. Additionally, the magnet
can be held stationary while the coil is rotated about its handle to produce a reading on the galvanometer.
Return the apparatus and magnet back to the demonstrations room.
Theory
When a magnet is moved near a coil, it increases the magnetic flux through the coil. The magnetic flux
through a single loop in the coil is
Z
→
− →
−
Φ=
B · dA,
(1)
area of loop
→
−
→
−
where Φ is the magnetic flux, B is the external magnetic field, and d A is the infinitesimal area vector of the
loop in the direction perpendicular to the plan of the loop. Michael Faraday (1791-1867) found that when the
flux through a closed, conducting loop of wire changes, an emf is induced in the loop.
The induced emf is
dΦ ,
(2)
=
dt where is the induced emf equal to the time rate of change of the flux through the loop. In the case of a coil
consisting of N loops, the induced emf is
dΦ .
(3)
=N
dt This induced emf drives an induced current to flow through the coil as defined by
Iinduced =
,
R
(4)
where Iinduced is the induced current and R is the resistance of the coil.
The direction of the induced current is found by Lenz’s law, which states that the induced current flows in
a direction so that it creates a magnetic field opposing the change in flux. Since a magnet’s field strength varies
with distance, there is a change in flux through the coil when the magnet is moving closer to or away from the
coil. Suppose a magnet is moving towards a coil as depicted in Figure 1. As the magnet is moving closer to the
coil there is an increase in flux flowing rightward through the coil. In order to oppose this increase in flux, the
induced current in the coil must flow in a direction so that a magnetic field pointing to the left is created. The
direction of the induced current is shown in Figure 1. In this demonstration, a galvanometer is connected to the
coil to detect the induced current.
If the motion of the bar magnet is reversed so that it is moving away from the coil, the magnetic flux flowing
rightward through the coil decreases. As a result, the induced current now reverses direction to create a magnetic
field pointing to the right in order to compensate for the decrease in flux. This reverses the polarity of the reading
on the galvanometer. A greater reading is registered by the galvanometer when the relative speed between the
magnet and coil is increased because the flux through the coil changes at a faster rate.
When the motion of the bar magnet ceases, the flux through the coil is no longer changing and the galvanometer
reads zero. The polarity of the reading on the galvanometer reverses if the orientation of the bar magnet is reversed
so that the opposite pole is now facing the coil.
A change in flux through the coil is also brought about when the orientation of the coil changes with respect
to the bar magnet. That is, if the bar magnet is held stationary and the coil is rotated about its handle, an
induced current is measured by the galvanometer. This is the principle behind the operation of a generator. In
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Coil
Motion of Magnet
S
N
Iinduced
Bexternal
Binduced
Figure 1: Diagram showing the induced magnetic field of a coil in a changing external magnetic field.
a generator, the rotation of a coil (which can be caused by wind turbines, water falling through a wheel, a hand
crank etc.) in a magnetic field induces a current in the coil. In an AC generator, the coil is connected to solid
slip rings and brushes which conduct the induced current through to a circuit.
When a coil is submerged in a uniform magnetic field, the flux through the coil given by Equation 1 becomes
Φ = A · B = AB cos θ,
(5)
where θ is the angle between the area vector and the magnetic field. Equation 5 can be written as
Φ = AB cos ωt,
(6)
where ω is the angular speed of the coil and t is time. It is worth noting that Equation 2, which calculates only
the magnitude of the induced emf can be written so that it determines the polarity of the emf (and thus, the
direction of the induced current) as well. In this form, Equation 2 is written as
=−
dΦ
.
dt
(7)
To understand how the negative sign is used to determine the polarity of the induced emf, consider a loop of wire
in an external magnetic field, as illustrated in Figure 2.
–+
+–
Bexternal
Negative Orientation
Positive Orientation
Figure 2: Diagram showing the positive and negative orientation of an induced current in a coil that is in a
changing external magnetic field.
First, the right hand rule is used to arbitrarily define a polarity for the loop. Pointing the thumb along the
direction of the applied magnetic field (in Figure 2 this is into the page, and in Figure 1 it would be in the
rightward direction), the direction in which the fingers curl establishes the ”positive” orientation of the induced
emf. That is, if the induced emf turns out to indeed be ”positive”, then the induced current would flow clockwise
as indicated.
Since a change in flux is required for an induced emf, suppose the magnetic field into the page in Figure 2 is
increasing in strength. Equation 7 is now used to determine the polarity of the induced emf. The time rate of
change of flux is a positive value because the field strength is increasing, but the negative sign in Equation 7 makes
the orientation of the induced emf ”negative”. Referring to Figure 2, it is seen that the ”negative” orientation
induces a counterclockwise current.
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It is often easier to use Equation 2 to calculate the magnitude of the induced emf and Lenz’s law to determine
the direction of the induced current, but Equation 7 is more useful in the case of a generator. To find the induced
emf in a generator, Equation 6 is substituted into Equation 7 and the emf is,
=−
d (AB cos ωt)
= ωAB sin ωt.
dt
(8)
Equation 8 shows that the generator actually produces AC voltage since the induced emf is a trigonometric
function.
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References
[1] Knight, Randall D. Physics for Scientists and Engineers, ”Magnetic Flux” 2nd ed, Calfornia: Pearson AddisonWesley, 2008. pg 1050-1052.
[2] Meiners, Harry F. Physics Demonstration Experiments Vol. II, ”31–2.2”, American Association of Physics
Teachers, The Ronald Press Company, New York, 1970. pg 932-933. .
[3] Sutton, Richard Manliffe. Demonstration Experiments in Physics, ”E-216. Induced Current from Relative
Motion of Magnet and Coil of Wire”, McGraw-Hill Book Company Inc, New York and London, 1938. pg 339.
[4] Hilton, Wallace A. Physics Demonstration Experiments at William Jewell College, ”E-8a Induced Current in
a Coil”, American Association of Physics Teachers, June 1982. pg 60.
[5] Jones, Chris. ”Understanding and using the minus sign in Faraday’s law”, Physics Education, November 2003.
pg 526-530.
[6] Knight, Randall D. Physics for Scientists and Engineers, ”Faraday’s law”, 2nd ed, California: Pearson AddisonWesley, 2008. pg 1055-1058.
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