Electromagnetic Induction
9. Electromagnetic Induction*
This session is for learning to use right-hand rules and learning Faraday’s law of induction. This
unit is not strictly in the problem-solving framework, but is an exploration.
The learning objectives are the following:
1. To be able to predict the direction of the magnetic field produced by a current in a coil
when the direction of the current is given.
2. To know how to calculate the direction of the EMF induced in a coil or around a closed
curve by a changing magnetic field.
3. To apply Faraday’s law to practical situations.
4. To know Lenz’ law and know how to apply it .
(This material is in your text. So lab sections can use the same conventions, we give
right-hand rules that may look different from ones in your text.)
Reading assignment: Review electromagnetic induction, Faraday’s law and Lenz’ law. Review
the magnetic field inside a solenoid.
Read the following sections. (Section numbers may be slightly different depending on the edition
of your textbook: Check the section titles.)
Serway and Vuille (212) 19.3 Magnetic Fields, 19.7 Magnetic Field of a Long, Straight Wire and
Ampère's Law, 19.9 Magnetic Fields of Current Loops and Solenoids, 20.1 Induced emf and
Magnetic Flux , 20.2 Faraday's Law of Induction, 20.3: Motional emf , 20.4: Lenz's Law Revisited
(The Minus Sign in Faraday's Law) , 21.7 The Tansformer
Serway and Jewett (252) 30.3 Ampre's Law, 30.4 The Magnetic Field of a Solenoid, 30.5
Magnetic Flux, 31.1 Faraday's Law of Induction, 31.2 Motional emf , 31.3 Lenz's Law, 31.4
Induced emf and Electric Fields , 33.8: The Transformer and Power Transmission
Three right-hand rules: Right-hand rules are absolutely necessary. The following three will be
used. The first is the rule for the direction of
A B :
C
B
A
Right-hand rule I:
1. Put the vectors tail to tail.
When you
write
2. A is the “first vector” because it is left of the “  ”.
3. Extend fingers of right hand along the first vector.
C  A B
4. Curl them into second vector ( B in this case).
5. Thumb points along the direction of the cross product
(which is
C
in this example).
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*© William A Schwalm 2012
Electromagnetic Induction
One use of the right-hand rule above is the magnetic force
F  qv  B .
Next is the right-hand rule to determine the direction of the magnetic filed produced by a current
carrying wire.
II. The magnetic-field right-hand rule:
1. Grab the wire carrying current by pointing the
thumb in the direction of the current.
2. Then the fingers curl in the direction of the
magnetic field.
III. The right-hand rule between oriented circles and areas they bound.
back
front
The thumb indicates the
direction of orientation of the
surface.
Consider a circular area and the circle that
bounds it. Suppose the curve is oriented as
shown. There is a right-handed relation
between the orientation of a loop and the
orientation of the area it bounds. This
means, you take your right hand and curl
the fingers around the curve in the direction
of orientation.
So, in this case the area bounded by
the curve is oriented “upward.” Keep in
mind that the right hand defines the
relation between the curve orientation
and the surface orientation.
One application of this is that a current going around a wire loop produces a magnetic field inside
the loop in the direction shown. Other applications will be seen below.
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Electromagnetic Induction
Pre-laboratory assigned problems:
1. Find a statement of Faraday’s law of induction in your textbook and give it here. Explain it as
necessary, referring to the third right-hand rule above. What does the term magnetic flux
mean?
2. Recall that the magnetic field
flows outward from the North
pole of a magnet. What do you
think will happen if you push the
magnet into the wire loop as
shown? Explain using
Faraday’s law and the right-hand
rule.
S
N
3. It is sometimes said that Lenz’ law is “really just the minus sign” in Faraday’s law. State
Lenz’ law about induced currents here and explain it referring to the second right-hand rule.
In-class exercises and problems: You will be using a bar magnet and a compass. Check to see
that the north pole of the compass actually points north. (The north pole of the earth is actually a
magnetic south pole!) Then, use the compass to determine which end of your magnet is north
and mark it somehow. In the figure, the north-seeking end of the compass needle (black) points
toward the south end of the magnet. Thus the taped end is the magnet’s north pole.
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Electromagnetic Induction
Now hold the north pole of your magnet against the page in the center of this circle:
(a) Does the magnetic flux go into the page or out of the page?
(b) Now, pull the magnet back toward you suddenly (carefully). Is the change in flux into or out
of the page?
(c) According to Faraday’s law, would the induced EMF drive a current in the loop clockwise or
counterclockwise?
Experiment 1: Electromagnetic induction by moving a bar magnet
(Review use of galvanometers in Bridge Measurement lab.) What should you expect when you
push the magnet into the coil? Before you try the experiment, record your predictions on the
white board.
S
N
In particular, to which side should the galvanometer needle
deflect? (To review how galvanometers work, recall the
Wheatstone bridge experiment.)
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Electromagnetic Induction
To work out a prediction, you might reason as follows:
(a) Which way will the magnetic flux pass through each turn of the coil, to the right or to the left?
(b) Will the flux through each loop be increasing or decreasing as you push the magnet in?
(c) So, which way will the induced EMF try to drive the current? (Remember Faraday’s law and
the right-hand rule for orientations.)
(d) Thus current will enter the galvanometer through which terminal?
Next, suppose you have pushed the end of the magnet
(e)the
Socoil.
which
wayleave
will the
deflect?
into
If you
at needle
rest in the
coil, will the
galvanometer be deflected to the right, to the left or not
at all? Explain.
N
Finally, if you were to pull the magnet back out of the coil, which way would the needle deflect?
Explain your prediction.
Now wire up the experiment and try out your prediction. If you didn’t find what you expected,
figure out why not and report it here.
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S
Electromagnetic Induction
Experiment 2. Electromagnetic induction by the electromagnetic coils
While Faraday’s law has to do with electric fields caused by changing magnetic fields, Ampere’s
law (in original form) says that an electric current will cause a magnetic field. The way this works
involves some other right-hand rules.
For instance, a current flowing in a long, straight wire induces a
magnetic field that circulates around the wire. The direction of
circulation is the direction the fingers of your right hand would go
around the wire with your thumb pointing along the current flow.
As a result of this, we can figure out that when a current flows around
in a loop it induces a magnetic field threading through the loop.
I
B
Imagine grasping the loop of wire shown with your right hand such that
your thumb aligns with the current. Would your fingers thread through the
area of loop into the page (a) into the page, or (b) out of the page?
Notice this is again the right-hand relation between magnetic field and
current. In this case, though, both field and current are constant in time,
unlike the situation for Faraday’s law.
When you form a coil of wire (insulated with enamel paint, so that the current does not take a
short cut, but must go around each loop of the coil) the result is the same as putting many current
loops together, so the magnetic fields add up. Now it is time to experiment with this idea. The
picture below shows a coil of wire, which is insulated with a thin, enamel coating, forming a coil.
When current flows through the coil, we anticipate it will act as an electromagnet.
I
Thus, when a current flows through a coil as shown
(Remember, the current must flow through a whole circuit,
and part of the circuit is not shown in order to simplify the
picture.) the resulting magnetic field is very similar to that of
a bar magnet, emanating from one end of the coil,
circulating around, and reentering the coil from the other
end.
In the cartoon at the right, the bar shown is NOT
a bar magnet, but a bar of “soft” iron. This can
be added to help concentrate the magnetic field
caused by the current flowing in the coil. With
the current flowing as shown, predict which end
will act as a north pole. (a) Right, or left?
I
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Electromagnetic Induction
By inspecting the coil you can determine how the current will circulate, provided you know which
terminal it enters. Recall that the current comes from the plus connection on the wall receptacle
and returns to the minus. (This means the electrons, with negative charge, must be moving in the
other direction.) Thus you can predict which end of the coil should be the North pole before you
connect the coil to the current source. Try this and see if you are right.
The tap switch in the photo is normally in the off position. After predicting the polarity of the
electromagnet, press the key to on and watch the action of the compass and the
galvanometer needle. Was your prediction correct? A soft iron “core” is inserted onto the coil
to increase the strength of the magnetic field. There are two keys G0 and G1 on the
galvanometer. Press first G1 key (less sensitive) . G0 key is sensitive. So, be careful not to
pin down the needle.
What happens when you reverse the direction of current flow in the coil by switching the wires?
What happens if you remove the soft iron rod? Is there still a field? Check carefully.
Next comes the most interesting set of experiments in which both Ampere’s law and Faraday’s
law are at work. The figure on the following page shows two coils, one large and one small, with
the smaller one placed inside the larger one. The inside coil contains a soft iron core to
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Electromagnetic Induction
concentrate magnetic flux, and it will act as an electromagnet that can be switched on and off.
The outer coil is attached to a galvanometer, as in the first experiment above on Faraday’s law.
Two lab partners are operating the circuit. One partner has just closed the switch while the other
operates the galvanometer.
Now in the space provided (or an additional page, if you need it) describe what happens when
you flip the switch on or off. Explain these phenomena in terms of the previous two exercises, i.e.
in terms of Faraday’s law and Ampere’s law. Try to go through all the steps of predicting which
way the needle will deflect in terms of which way the current flows, starting from the wall. Write in
complete sentences, as part of your grade will depend on the quality of your explanation.
Experiment 3, step-up transformer:
OFF
V
a.c.
source
V
A
Np
NS

V
A
COM
A
10A

One practical application of Faraday's Law is a transformer. The figure above is an idealized
step-up transformer. The central idea of the transformer is that there are two coils or windings,
electrically insulated from each other but wound on the same core typically made of a material
such as iron. The primary coil is connected to an AC source. Alternating current (a.c.) in the
primary coil causes time varying magnetic field which passes through the secondary coil. The
metal core acts to focus the magnetic field in such a way that the same flux passing through each
turn of the primary coil also passes through each turn of the secondary. Since the magnetic field
is time varying, the magnetic flux passing through the secondary coil is time varying. The
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Electromagnetic Induction
Faraday's law states that when a time varying magnetic flux passes through the closed,
conducting loop an EMF is created. Thus even no though no external electric source is connected
to the secondary coil a time varying electric current appears in the secondary coil. Because
exactly the same flux passes through each turn of the primary and each turn of the secondary,
the EMF per turn is the same, so the ratio of the primary to secondary voltages should equal the
ratio of the numbers of turns.
Np
Ap
NS
Vs
Vp
Set voltage to
high scale.
Set voltage to
low scale.
(a) Using the schematic above as a guide, connect an AC ammeter in series with the primary
windings and an AC voltmeter across the primary winding, in such a way that it will measure
current through the primary. Select the voltage scale to 20V max. Connect a second AC
voltmeter across the secondary windings and select the scale to 200V max. After checking
with your lab TA, connect the primary side to a 60 Hz AC-source.
Record the meter
readings.
Vp =
Ip =
Vs =
(b) For an ideal transformer, when the input is purely sinusoidal and not too much current flows
in the secondary, the ratio of the primary potential V p to the secondary potential Vs is the
same as the ratio of the number of windings of the primary to the number of windings in
secondary coils. So,
Vp
Vs

Np
Ns
From your measurements, determine the ratio Ns /Np.
(c) For an ideal transformer, the power output at the secondary is equal to the power input at the
primary. Determine the resistance R of the voltmeter in the secondary circuit from your
measurements of Ip, Vp and Vs. Does this agree with what you would expect for a voltmeter
resistance?
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Electromagnetic Induction
Examine the transformer you have been given and see if you can find information on it that will let
you estimate the turns ratio as an independent check of what you have done.
Suppose you find the information printed on the transformer seems to indicate a different turns
ratio than the one you compute from voltage measurements. Can you think what might be going
on? Discuss this with your team members and write your ideas here.
Figure out a way to check this by making another measurement. Describe what you will do and
give the result here. What is the final verdict on the turns ratio?
At the end of the period there will be a breif discussion of how the lab activities you have been
engaged in relate to the learning objectives. Summarize this discussion in your report, adding
your own comments as you see fit.
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