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General Physics II
Electromagnetic Induction and
Electromagnetic Waves
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Induced emf
• We have seen that an electric current produces a
magnetic field. Michael Faraday demonstrated that
a magnetic field can be used to generate, or
induce, an emf, which in turn can produce a
current in a conductor. The process of inducing an
emf with a magnetic field is called electromagnetic
induction.
• The best way to demonstrate electromagnetic
induction is to conduct experiments (as Faraday
did).
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Electromagnetic Induction Experiments
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Induced emf
Our observations indicate that a current, and
hence an emf, is induced in a conducting loop
when:
• The loop moves relative to a steady non-uniform
magnetic field. The faster the motion, the greater
the magnitude of the induced emf. The direction
of the induced emf reverses when the direction of
motion reverses. If there is no motion, there is no
emf.
• The magnetic field changes within the stationary
loop. The faster the change, the greater the emf.
The direction of the induced emf reverses when
the sign of the change in the field reverses. If
there is no change, there is no emf.
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Motional emf
• Consider a conductor of length
l that moves in a
G uniform
G
magnetic field B with velocity v
that is perpendicular to the
field. We assume by
convention that the charge
carriers in the conductor are
positive.
• As the conductor moves, the
charges move with it. The
movement of the charges
within the magnetic field
produces a magnetic force,
which drives the charges along
the length of the conductor (in
this case, upward).
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Motional emf
• The positive charges accumulate at the top, leaving a net
negative charge at the bottom. This creates an electric field
that exerts a downward electric force on the charges in
opposition to the magnetic force.
• Eventually, the forces become equal in magnitude and the net
force on a charge carrier is then zero. There is no further
charge accumulation. At this point,
FE = qE = FB = qvB
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⇒
E = vB.
Motional emf
• Note that the conductor is very
much like a battery. A nonelectrostatic force (the magnetic
force) causes charge separation
leading to an electric field and
potential difference. The work done
per unit charge by the magnetic
force is the emf of the conductor.
This emf is equal to the potential
difference between the top and
bottom (“terminals”) of the
conductor:
E = ΔV = El.
⇒ E = vlB. (Motional emf)
(Valid for a straight conductor with velocity
perpendicular to the magnetic field.)
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Motional emf in a Circuit
• If a straight wire slides over a Cshaped conducting rail in a magnetic
field, the motional emf of the sliding
wire will cause a current to be
established in the circuit.
• The current is given by
G
Fmag
G
Fpull
I = ΔV = E = vlB ,
R R R
• where R is the total circuit resistance.
• The current in the moving wire
causes a magnetic force in the
direction opposite Gits velocity. Thus,
an external force F pull is necessary to
prevent the wire from slowing down
and stopping.
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Workbook, Chapter 25, Questions 1, 2, 3
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Generator
• A generator converts mechanical energy into electric energy.
One of the most common methods is via the motional emf
produced by a coil rotating in a steady magnetic field.
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Magnetic Flux
• We have seen that moving a magnet into or out of a
stationary conducting loop and moving the loop into or out of
a steady magnetic field generates an induced current in the
loop. It turns out that a current can be induced in a conducting
loop in other ways, such as:
• Rotating the loop within a steady magnetic field (as we have
seen in the operation of a generator);
• Changing the area of the loop in a steady magnetic field;
• Immersing the loop in a time-varying magnetic field (e.g.,
produced by solenoid whose current changes with time).
• All cases in which a current is induced in a conducting loop
(due to the presence of an induced emf) can be described by
changes is a single quantity called the magnetic flux.
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Magnetic Flux
• The magnetic flux is proportional to the number of magnetic
field lines going through a loop.
• The greater the (i) magnetic field and (ii) area of the loop
exposed to the field, the greater the magnetic flux.
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Magnetic Flux
• The magnetic flux Φ is defined as
Φ = AB cosθ ,
where A is the area of the loop, B is the magnetic field, and θ
is the angle between the axis of the loop and the magnetic
field.
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Workbook: Chapter 25, Question 4
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Lenz’ Law
• The utility of the concept of magnetic flux is that it allows us to
make a simple statement that encompasses all the
magnetically-induced current experiments we have seen:
• A current is induced in a closed conducting loop whenever
there is a change in the magnetic flux through the loop.
• Lenz’s law tells us the direction in which the induced current
will flow. Lenz’s law states that
the induced current flows in a direction such that its own
magnetic field opposes the change in magnetic flux that
produced the current in the first place.
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Applying Lenz’s Law
G
Binduced
Induced
current
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Workbook: Chapter 25, Question 5
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Faraday’s Law
• In our induction experiments, we saw that the more rapidly
the magnetic flux changes through a conducting loop, the
greater the induced current. The greater induced current is
due to a greater induced emf. Faraday’s Law gives us a
quantitative statement of the relationship between the
induced emf and the rate at which the magnetic flux
changes.
• Faraday’s Law states that the induced emf in a loop is equal
to the magnitude of the rate of change of the magnetic flux
through the loop. The emf is in the same direction as the
induced current given by Lenz’s law.
• Mathematically, Faraday’s law for a single loop is written as
E = ΔΦ .
Δt
For an N-turn coil, we have
E = N ΔΦ .
Δt
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per turn
Workbook: Chapter 25, Question 6, 7
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Textbook: Chapter 25, Problem 12
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Eddy Currents
• If the magnetic flux changes
through a bulk conductor (e.g., a
sheet of metal), currents will be
induced. These currents are not
confined to single loops. Rather
they are distributed over the
region in which the magnetic flux
changes. Such currents are
called eddy currents.
• Consistent with Lenz’s law, the
magnetic force acting on the
conductor due to the eddy
currents opposes the motion of
the conductor. This is useful for
magnetic braking.
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