Resource Lesson
Motional EMF
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As stated in our previous introductory lesson on induced emf,
Faraday's Law of Induction
states
ε
= -N(ΔΦ/Δt)
where
ε
is the induced voltage in a coil, measured in volts
N is the number of loops in the coil
Φ is the number of flux lines, Φ = B
_{perpendicular}
A
ΔΦ is the changing flux, measured in webers
Δt is the time over which the change occurs, measured in seconds
When the number of flux lines is constant, no emf is induced in a coil. The number of flux lines can be changed in two ways:
by changing the strength of the magnetic field OR
by changing the area of the coil.
In this lesson we will investigate the second case when an emf is induced by changing a loop's cross-sectional area that is exposed to a constant external magnetic field. This is called
motional emf
.
The following
physlets
show two ways of changing the coil's area and the resulting induced emf:
flexing coil
moving coil
Sample Problem
In the following diagram, suppose that the green cross bar is moving to the right at a constant velocity,
v
. As it moves, the area of the "loop" presented to the magnetic field (+z) increases consequently allowing more flux lines to pass through the "loop" and generating an emf in the "loop."
ε
= -N(ΔΦ/Δt)
ε
= -N (B
_{perpendicular}
ΔA) /Δt
ε
= -NB
_{perpendicular}
(
Δw) /Δt
ε
= -NB
_{ perpendicular}
(Δw/Δt)
ε
= -NB
_{ perpendicular}
v
and obeys the formula
motional
ε
= - NB
_{perpendicular}
v
The right-hand curl rule is used to determine the direction of the induced emf/current. In this formula,
v
is the constant velocity in m/sec with which the loop is moving into or out of the magnetic field and
is the length of the side of the loop which does not change.
As the bar moves to the right, will a clockwise or counterclockwise current be induced in the left side of the coil?
Calculate the amount of force required to keep the bar moving at a constant velocity.
As the bar moves to the right, calculate the amount of electrical power dissipated through the resistor.
We will now look at these two AP essays to verify that you understand the principles of induced emf.
1982 B5
1986 B4
Related Documents
Lab:
Labs -
Telegraph Project
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Special Case of Induction
RL -
Eddy Currents plus a Lab Simulation
RL -
Electricity and Magnetism Background
RL -
Generators, Motors, Transformers
RL -
Induced Electric Fields
RL -
Induced EMF
RL -
Inductors
RL -
LC Circuit
RL -
Maxwell's Equations
RL -
RL Circuits
Review:
REV -
Drill: Induction
Worksheet:
CP -
Induction
CP -
Power Transmission
CP -
Transformers
NT -
Induction Coils
WS -
Induced emf
WS -
Practice with Induced Currents (Changing Areas)
WS -
Practice with Induced Currents (Constant Area)
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