Physics 12
Electromagnetic Induction
In 1819, when Oersted demonstrated the ability of a steady current to
produce a steady magnetic field, scientists assumed that a steady magnetic field
would produce a steady current. It seems logical and yet it doesn’t work. It wasn’t
until 1831 that Michael Faraday discovered the basic principle of electromagnetic
induction. Faraday went on to develop the first electric generator, modern versions
of which are now used to provide electricity to homes and industries all over the
world.
Faraday’s Law of Electromagnetic Induction
Faraday made his discovery by experimenting with conductors in the vicinity of
magnetic fields. His investigations involved three situations:
i) moving a wire through the jaws of a horseshoe magnet
ii) plunging a bar magnet into and out of the core of a coil
iii) touching the iron core of a coil with a bar magnet, then removing the magnet
In the first case, Faraday found that electric current only flowed while the
conductor was cutting across the magnetic field. In the second case, electric current
only began to flow when the bar magnet was moving into or out of the coil. And in
the third situation, electric current was observed in the coil when the iron cylinder
was being magnetized or demagnetized.
Faraday was able to combine these three conditions into one general
statement, now known as the law of electromagnetic induction.
Law of Electromagnetic Induction
An electric current is induced in a conductor whenever the magnetic
field in the region of the conductor changes.
Induction can be demonstrated with a device that Faraday constructed and
used himself in his early studies of the induction effect. Known as Faraday’s iron ring, it consists
of a doughnut-shaped ring of soft iron with two separate coils of wire wound around it, as in
Figure 4.
The primary coil is connected through a switch to a voltage source. The secondary
coil is connected directly to a galvanometer (a device for measuring current). When the switch is
closed there is a current in the primary circuit, causing the entire iron ring to become magnetized.
This sudden increase in magnetic field strength causes a current to be induced momentarily in the
secondary coil. Once the current in the primary coil is steady and the magnetic field in the iron ring
is established, the induced current no longer exists.
If the switch is then opened, the iron ring becomes demagnetized and the consequent
decreasing magnetic field strength once again induces a momentary current in the secondary coil,
this time in the opposite direction. This effect is known as mutual induction. In fact, the two coils
do not have to be coupled with an iron ring; the iron ring merely acts to strengthen an effect that
would be present in any case.
By observing what happens when a bar magnet is plunged into the core of a coil that is connected
to a galvanometer, it is possible to conclude that the factors affecting the magnitude of the induced
current are
• the number of turns on the induction coil
• the rate of change of the inducing magnetic field
• the strength of the inducing magnetic field
Faraday’s discovery of induced currents opened the door to readily accessible and
cheap sources of current. This current could be used to power electric motors and other devices,
saving time and money for many people and industries. However, there were still some questions
to be answered. What determines the direction of the induced current? Where does
the energy associated with the induced current come from ?
A few years after Faraday’s discovery of induction, a German physicist working in
Russia, Heinrich Lenz (1804–1865), applied the law of conservation of energy and succeeded
in stating this relationship.
Lenz (pronounced “Lents”) reasoned that when a current is induced through a
conductor, the induced current itself sets up a magnetic field. This magnetic field, which we will
call the induced field, then interacts with the inducing field, either attracting it or repelling it. In
determining which of these interactions is the more likely one, it will help to consider an example.
When the N-pole of a bar magnet enters a coil, a galvanometer will indicate an
induced current through the coil. When the N-pole is removed, the galvanometer will indicate a
current in the opposite direction. Using the S-pole of the bar magnet causes induced currents in
directions opposite to the above. Evidently there is some simple relationship between the action of
the inducing field and the direction of the induced current.
Lanz’s Law is really an application of the Law of Conservation of Energy. Energy cannot
be created nor destroyed. You cannot get electrical energy from nothing. It must come from
somewhere. As indicated in diagram (a), in order to see work done, the right hand side of the core
must be the same pole as the approaching pole, otherwise “S” will attract the incoming N pole, and
“energy” of plunging in the bar magnet will not be needed.
Similarly, when the bar magnet is being pulled away, in order to see “work done”, the
right hand side of the core must be south pole, so that work is needed to overcome the attraction.
Lenz’s Law
For a current induced in a coil by a changing magnetic field, the
electric current is in such a direction that its own magnetic field
opposes the change that produced it.
It should be noted that Lenz’s law is really just a rule to determine the direction of the
induced current and contains nothing that wasn’t already implied by Faraday. Also, the changing
magnetic field really produces an electric field, and the induced current is just a way that it can be
detected.
Example 1) Determine the direction of the electric current for the case in Figure below.
Example 2) Determine the pole of the bar magnet that is being inserted into the induction coil in
Figure.
In the same way, if a conducting rod is moved through a magnetic field, the magnetic
field of an induced current opposite the magnetic field that produced the induced current (Lenz’s
law).
Direction of current:
 Palm opposite velocity (v)
 Fingers into the page
 Thumb will point up in direction of current.
Lenz’s law tells us that the magnetic force on the conducting rod must be in the
opposite direction to its motion (opposite to V). If we use our right hand (opened) and point the
palm opposite to V and our fingers in the direction of the induced current. In the diagram above,
the current flows counter-clockwise through the circuit.
Now it is your term to determine how the induced current flow in the given diagram
below.
What is the magnitude of the induced current?
The magnitude of the induced current is found using Ohm’s law.
and
V=IR
V = B┴ l v
where V = induced voltage
B┴ = magnetic field component perpendicular to………
l = length of the conducting rod
v = speed of the conducting rod
Derivation of V = B┴ l v
(Method I)
When a conducting rod is moved through a magnetic field, the + charges in the rod experience a
magnetic force.
F = q v B┴
These positive charges would move to the upper end of the rod, leaving the bottom end
negative. Because of the difference in charge between the ends of this rod, there is a potential
difference (induced voltage). When the positive charges were forced through this rod, work is
done.
W=Fd
or
∆E = F l (l = length of the conductor)
but
F = Fm = q v B┴ and ∆E = q V
therefore q V = q v B┴ l
to simplify
V = v B┴ l
Derivation of V = B┴ l v
(Method II)
To derive this equation we can use the concept of magnetic flux (Φ).
Faraday’s law of induction: The induced voltage is proportional to the rate of change in
the magnetic flux (Φ).
Now let us return to our circuit:
Change in magnetic flux:
∆ Φ = B┴ l ∆ x
Rate of change in magnetic flux:
Since
x
= v , then
t
V = B┴ l v
Example 1) A conducting rod 25.0 cm long moves perpendicular to a magnetic field, B = 0.20 T at
a speed of 1.0 m/s. Calculate the induced voltage in the rod?
Example 2) The conducting rod in the diagram below is 15 cm long, and is moving at a speed of
2.0 m/s perpendicular to a 0.30 T magnetic field.
If the resistance in the circuit is 4.0 Ω, what is the
magnitude and direction of the current (electron
flow) through the circuit?
Example 3) A rectangular coil of wire containing 5 loops is moved at a speed of 4.5 m/s
perpendicular to a 0.85 T magnetic field as shown below. If the length of the side of the
coil moving perpendicular to the field is 0.28 m and the resistance in the circuit is 3.0 Ω.
a) What is the induced current?
b) What is the direction of the current (electron flow)?
Example 4) A solid conductor travels 15 m/s across a uniform 0.086 T magnetic field. Which side
(X or Y) is positively charged and what is the emf across this conductor?
Example 5) A 600 turn circular coil with an area of 2.64 x 10–2 m2 is perpendicular to a 0.08 T
field. The magnetic field changes to 0.01 T in the opposite direction in 0.25s.