Download Induced EMF and Induced Current

Electromagnetic Induction
From early on, it was noticed that a moving current
could produce a magnetic field. This was first discovered
by Oersted if you recall.
The question was then asked, “If a moving current can
produce a magnetic field, is there any way a magnetic field
can produce a current?” That is, can the process be
reversed?
The answer is yes! It turns out that a moving, or
changing, magnetic field can produce a current in a wire.
The following diagram illustrates the procedure:
Induced EMF and Induced Current
The current that is set up in the coil is called an
induced current, because it was brought about (or
induced) by a changing magnetic field. (Recall charging by
induction as an analogy.)
Since a source of emf is always needed to produce a
current, the coil itself behaves as if it were a source of emf.
Therefore, it is known as the induced emf.
Q: How was EMF defined?
Remember that all we need to produce an electric
current is a changing magnetic field. So, another way of
changing the magnetic field is by changing the area of the
coil in a constant magnetic field. The following diagram
illustrates this:
Induced EMF and Induced Current
Finally, we can also generate an induced current when
a coil or constant area is rotated in a constant magnetic
field and the orientation of the coil changes with respect to
the field. The following diagram illustrates this:
If the rotation stops, the current vanishes.
Changing the magnetic field, changing the area of the
coil, and changing the orientation of the coil are all
methods that can be used to create an induced emf. The
phenomenon of producing an induced emf with the aid of a
magnetic field is called electromagnetic induction.
Motional EMF
How can this be useful to us? We first start with the
case in which a conductor is moving in a constant magnetic
field.
A conducting rod moving in a magnetic field has an
induced emf produced inside the rod. The reason an emf is
produced comes from the magnetic force on each charge in
the rod:
The velocity v of the rod is constant and is
perpendicular to the magnetic field B. Each charge q feels
a magnetic force of F=qvB.
Q. In which direction is the force acting?
A. Towards the center of the page!
Thus, a current will be set up!
This type of induced emf is called motional emf
because it will remain so long as the rod is in motion.
The magnitude of the induced emf is proportional to
the velocity, magnetic field and the length of the rod:
E = vBL
Q. Can you think of an application of this process?
A. Production of an alternating current!
If I constantly move the bar back and forth, I will
constantly be changing the direction of the current! Thus, I
will produce an alternating current in the circuit.
In solving problems, we can use for example Ohm’s
law but with:
V=IR
V=vBL
As well as all the other equations we used.
Magnetic Flux
Motional emf, as well as any other type of induced
emf, can be described in terms of a concept called the
magnetic flux.
Magnetic flux is analogous to the electric flux as it
deals with the electric field and the surface through which it
passes. (Recall Gauss’ Law! AHHHH!)
Magnetic flux is defined in a similar way. It is defined
as the number of “magnetic field lines” passing through a
given area.
We define the magnetic flux, , as BA where B is the
magnetic field and A is the area through which it passes.
We can write the induced emf as then:
E = vBL = (x/t)BL = (xL/t)B = AB/t = t
General Expression for the magnetic flux
In general, the magnetic flux is the number of field
lines that are passing through an area, perpendicular, to
the field:
So, in general, we can write:
BA cos 
Q. What are the units of magnetic flux?
A. T-m2 which is a unit called a Weber (Wb) after the
German physicist Wilhelm Weber.
Faraday’s Law of Induction
Looking at the situation above, we see that the current
flow is counterclockwise through the circuit as the
conductor is moved to the right.
However, using the “other” right hand rule, in what
direction should the current flow in the circuit?
The answer is clockwise! Heinrich Lenz first noticed
this so it is known as Lenz’s Law.
In our definition of the induced emf of a circuit, we
must make the following correction to the equation in order
to get the direction of the current correct:
E = - /t
So the induced current will flow in the opposite
direction to the changing magnetic field.
Faraday went one step further when he noticed that the
induced emf is not only dependent on the changing flux but
also on the dimensions of the wire loop.
Specifically, the emf increased as the number of loops
in the coil. Therefore:
E = - N (/t)
There are many applications to the physics of
electromagnetic induction including:
 Electric guitars
 Tape decks
 Microphones
However, we will now focus on how we can use this
physics to make an ac generator.
The Electric Generator
In essence, we already discussed how an ac current
could be produced using the concepts of induced currents
and emfs.
In it simplest form, an ac generator consists of a coil
of wire that is rotated in a uniform magnetic field.
Either an engine or some other mechanical means
(such as moving water…) then rotates this coil of wire.
As the coil rotates, the changing orientation of the coil
produces a changing magnetic flux and thus an induced
emf.
It changes according to the following equation:
E = BLv sin 
Upon the substitution of many quantities including
changing from a translational to a rotational velocity, we
find:
E = NAB  sin t
where f the angular velocity and f is the frequency in
Hz.
Mutual and Self Inductance
We have seen that an emf can be induced in a coil by
keeping the coil stationary and moving a magnet nearby, or
by moving the coil near a stationary magnet.
However, we illustrate even another way of producing
an induced emf.
A primary coil is connected to an ac generator and the
secondary coil is attached to a voltmeter.
The changing current in the primary coil creates a
changing magnetic field that in turns produces an induced
emf in the secondary coil.
The effect in which a changing current in one circuit
induces an emf in another is called mutual induction.
Self Induction
In all the examples of induced emfs presented so far,
the magnetic field has been produced by some external
source, such as a permanent magnet or an electromagnet.
However, let us investigate the following situation.
We know that if we attach a coil to an ac generator, we will
produce a magnetic field that follows from the right hand
rule.
However, because it a changing magnetic field, it will
induce a current in the wire that will be in the opposite
direction of the current from the generator in accordance
with Lenz’s Law. Thus, an induced emf is produced
The effect in which a changing current in a circuit
induces an emf in the same circuit is referred to as selfinduction.
Inductance and Inductors
How easily, or how strong, the induced emf is
generated in the coil (solenoid) is called the inductance of
the coil. The coil is called an inductor, which is just
another name for a solenoid.
The units of inductance are V-s/A, which is called a
henry. The size of the emf that is produced in a coil is
given as:
E = -L (I/t)
L is the inductance
An inductor, like a capacitor, can store energy. This
stored energy arises because a generator does work to
establish a current in an inductor.
The energy stored in an inductor is given as:
Energy = ½ L I2
Transformers
One of the most important uses for self and mutual
inductance takes place in a transformer. A transformer is a
device for increasing or decreasing the amount of voltage
in a device.
For example, your wall socket carries a voltage of
120V. Yet you have done HW problems that state
electrons passing through a picture tube in a TV pass
through a potential of 15,000 V. Where did the extra
voltage come from?
It comes from Faraday’s law. Let’s take the TV
example and see where the extra voltage comes from.
Faraday’s law says that:
E1= -N1 (/t)
If I attach another coil, the same (/t) will pass
through it but if I vary N, the new emf will be:
E2= -N2 (F/t)
To find the increase/decrease in voltage, we take the
ratio of the 2 to find:
E2/E1 = N2/N1
So the increase the voltage difference will be:
E2 = (N2/N1) E1
Power companies use “step up” transformers to pass
current through power lines and then in you neighborhoods
you have “step down” transformers to return the 120V
potential increase from the power plant.