PS114
Chapter 22
Electromagnetic Induction
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Induced emf E and induced current I
• There are many ways a magnetic field can be used to generate an electric
current. The ability to produce electrical energy and transport it long
distances has had a profound impact on our civilization. The physics
describing the production of electrical energy was probably the greatest
discovery of the 19th century.
• Demonstration: Moving a magnet in and out of a conducting coil
induces a current.
• The coil behaves as an emf source. This emf is known as an induced
emf.
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Motional emf
• One form of induced emf is called motional emf. A circuit is formed
by placing a conducting bar on a conducting rail of width L. A magnetic field B is directed perpendicular to the area of the circuit and
the conducting bar is caused to move at a velocity v. The motional
emf occuring as a result of the motion of the bar is:
E = vBL
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Problem 4:
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In 1996 NASA performed an experiment, called the Tethered
Satellite experiment. In this experiment a 2.0 × 104 -m length
of wire was let out by the space shuttle Atlantis to generate
a motional emf. The shuttle had an orbital speed of 7.6 ×
103 m/s, and the magnitude of the earth’s magnetic field at the
location of the wire was 5.1 × 10−5 T. If the wire had moved
perpendicular to the earth’s magnetic field, what would have
been the motional emf generated between the ends of the wire?
Magnetic flux
• In order to study how induced emf’s are produced (E), we need to introduce the concept of magnetic flux.
• The magnetic flux Φ is defined as the product of the magnetic field B
passing through a surface area A. This can be written as:
Φ = BA cos θ
~ vector and the A
~ vector. The area
where θ is the angle between the B
vector is a vector whose length is proportional to the area and whose
direction is perpendicular to the surface area through which the magnetic
field passes.
• There are 3 ways to change the flux, ∆Φ.
1. Change the strength of the magnetic field B,
2. Change the size of the area A, and
3. Change the orientation of the area A with respect to the magnetic
field B.
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Problem 10:
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The drawing shows two surfaces that have the same area. A
uniform magnetic field B fills the space occupied by these surfaces and is oriented parallel to the yz plane as shown. Find
the ratio Φxz /Φxy of the magnetic fluxes that pass through the
surfaces.
Faraday’s law of electromagnetic induction
• Faraday’s Law was probably the most important scientific
discovery of the 19th century.
Faraday’s Law: the average emf E induced in a coil of N
loops is:
∆Φ
E = −N
(1)
∆t
where ∆Φ is the change in magnetic flux through one loop
and ∆t is the time interval during which the change occurs.
The SI unit of Emf: is the volt (V )
Problem 18:
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In each of two coils the rate of change of the magnetic flux in
a single loop is the same. The emf induced in coil 1, which has
184 loops, is 2.82 V. The emf induced in coil 2 is 4.23 V. How
many loops does coil 2 have?
Lenz’s law
• We are not covering this section.
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Applications of electromagnetic induction to the reproduction of sound
• We are not covering this section.
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The electric generator
• The electric generator is the primary source of electrical energy in our
world today. Hydroelectric power is electrical energy produced from
converting the potential energy of water to kinetic energy, and then,
using the kinetic energy to turn a turbine that contains conducting coils
rotating between large, constant magnetic fields.
• The electric generator works on the principle described by Faraday’s Law
where the magnetic flux is changing due to the rotation (i.e., changing
orientation) of the coils. The emf induced in a rotating planar coil is:
E = N ABω sin(ωt) = Eo sin(ωt)
where ω = 2πf and Eo = N ABω is the peak voltage. The typical ac
frequency in the United States is f = 60 Hz
Problem 37:
One generator uses a magnetic field of 0.10 T and has a coil area
per turn of 0.045 m2 . A second generator has a coil area per
turn of 0.015 m2 . The generator coils have the same number
of turns and rotate at the same angular speed. What magnetic
field should be used in the second generator, so that its peak
emf is the same as that of the first generator?
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Mutual inductance and self-inductance
• We are not covering this section.
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Transformers
• We are not covering this section.
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