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Physics 272
March 7
Spring 2017
http://go.hawaii.edu/j8M
Prof. Philip von Doetinchem
[email protected]
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Electromagnetic induction
http://www.youtube.com/watch?v=hajIIGHPeuU
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Electromagnetic induction
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Demo 1:
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magnet moved in
→ magnetic flux through solenoid changes
→ induced current appears
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The faster the magnet the higher the induced current
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If solenoid is approached first with the other magnetic
pole, the direction of the induced current changes
–
When magnet is moved away from the solenoid the
direction of the current changes again.
Demo 2:
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Same as demo 1, but using a different coil and a digital
multimeter.
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Electromagnetic induction
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Demo 3:
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two solenoids: one large one connected in a simple circuit
and a
second, smaller one, connected to an ammeter
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When switch is closed
→ a DC current is established in the circuit
→ steady magnetic field is produced in the large solenoid
→ no induced current in the small solenoid as the
magnetic flux through it does not change
–
when switch is switched on or off
→ an induced current is produced
→ for a short period of time the current changes
→ magnetic field is produced by the large solenoid
changes as well
→ induced current in the small solenoid.
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Electromagnetic induction
https://phet.colorado.edu/sims/html/faradays-law/latest/faradays-law_en.html
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Generator
https://phet.colorado.edu/en/simulation/generator
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Changing magnetic flux
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The key component is the changing magnetic flux
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Flux changes caused by
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magnetic field changes with time
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coil moves through a non-uniform magnetic field
The changing flux causes an induced electromotive
force
–
Proportional to the rate of change of magnetic flux
through the coil
–
Direction of the induced emf depends on if the flux is
increasing or decreasing
–
No flux change = no induced emf
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Faraday's law
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Induction is a very important
effect that is widely used
Electric generators produces emf
by varying magnetic flux through
coils of wire
Source: http://de.wikipedia.org/wiki/Elektrischer_Generator
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Basic concept: changing magnetic flux through a circuit
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Faraday's law of induction:
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The induced electromotive force in a closed loop equals the
negative of the time rate of change of magnetic flux through the
loop.
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Lenz's law
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The direction of any magnetic induction effect
is such as to oppose the cause of the effect
Cause can be
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Changing flux due to varying magnetic field
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Changing flux due to motion of conductors
Think about it like: induced current tries keeping Source: http://de.wikipedia.org/wiki/Emil_Lenz
the system in the state it was before the flux
Heinrich F. E. Lenz
change happened.
1804-1865
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Example: Emf and current induced in a loop
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Uniform magnetic field
between poles of
electromagnet, which's
magnitude is increasing by
0.020T per second
Coil with area of 120cm2 is
in this field, total resistance
5W → What are emf and
current in the loop?
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A simple alternator
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An alternator is a device that
generates emf
By Arthur Kronenberger (www.physik3d.de) [CC BY-SA 3.0 de (http://creativecommons.org/licenses/by-sa/3.0/de/deed.en)], via Wikimedia Commons from Wikimedia Commons
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A simple alternator
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Emf is sinusoidal with time → alternating current
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Plane perpendicular to magnetic field: maximum(minimum) flux
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Plane (anti)parallel: zero flux
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Fastest change when plane (anti)parallel
when angular speed is doubled the rate of change of the flux
doubles and this causes the induced emf and induced current
to double
→ torque required is proportional to the current in the loop, so
the torque also doubles
Careful:
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Electromotive force is not created out of nowhere
–
Energy must be conserved and energy has to be supplied to
make the loop spin → energy conversion
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Slidewire generator
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Look at individual charge in
slidewire:
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Feels magnetic force
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Separates charges
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Builds up electric field
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Equilibrium between electric
force and magnetic force
(→ also see Hall effect)
x
No magnetic forces act on
the charges in the
stationary U part, but
sliding rod creates
potential difference (source
of emf)
→ establishes current
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Motional electromotive force
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Origin of electromotive force is of non-electrostatic
nature
Charges are brought to a higher potential
Concept can be generalized to conductors of any
shape and in any field (can be non-uniform, but not
varying with time)
–
take the perpendicular projection of the velocity with
respect to the magnetic field (cross product)
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Use the parallel projection of the former along a line
element of the conductor (scalar product)
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Example: Bar on inclined plane
Calculate the power dissipation at terminal speed.
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Example: Bar on inclined plane
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Example: Bar on inclined plane
Horizontal component of the gravitational force:
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Example: Bar on inclined plane
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