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Electromagnetic Induction
AP Physics
Chapter 21
Electromagnetic Induction
21.1 Induced EMF
Induced EMF
Michael Faraday – a changing magnetic field
can produce an electric current
This is an induced current
21.1
Induced EMF
A magnet moved quickly into a coil of wire
induces a current
When it is quickly moved the other way, a
current is induced in the opposite direction
21.1
Electromagnetic Induction
21.2 Faraday’s Law of Induction;
Lenz’s Law
Faraday’s Law of Induction; Lenz’s Law
From experiments the induced emf depends
on
1. Rate of change of the magnetic field
2. Loop’s area
3. Angle
Magnetic flux is the
total number of
magnetic field line
passing through
the are enclosed by the loop
21.2
Faraday’s Law of Induction; Lenz’s Law
Magnetic Flux
 B  BA cosq
When q is 90, no field lines pass through the
loop
The unit for magnetic flux
is a weber
21.2
S-136
A wire that forms a loop that is 25 cm on a
side and is placed in a 4T magnetic field.
A current of 10 A is then run through the
wire. What is the maximum and minimum
torque that can be
applied to the wire
under these
circumstances?
Faraday’s Law of Induction; Lenz’s Law
Since the induced EMF is the rate of change
of flux
 B
 
t
This is Faraday’s Law of Induction
For multiple loops in a magnetic field
 B
  N
t
Where N is the number of loops in the field
21.2
S-138
A wire loop with a diameter of 25 cm goes from
being perpendicular to a magnetic field to
parallel in 0.3s. The field strength is 10T.
A. What is the change in magnetic flux?
B. What is the induced EMF?
C. If the field points into the
board, and the left side of
the loop is rotation out of the
board, what is the direction
of the induced current?
Faraday’s Law of Induction; Lenz’s Law
Lenz’s Law – a current produced by an
induced emf moves in a direction so that its
magnetic field
(produced by
the current)
opposes the
original change
in flux
21.2
Faraday’s Law of Induction; Lenz’s Law
Steps in problem solving – Lenz’s Law
1. Determine if the magnetic flux inside the
loop is decreasing, increasing, or
unchanged
2. The magnetic field due to the induced
current
a. Points in the same direction as the
external field if the flux is decreasing
b. Points in the opposite direction if the
flux is increasing
21.2
Faraday’s Law of Induction; Lenz’s Law
Steps in problem solving – Lenz’s Law
3. Use the right hand rule-1 to find the
direction of the induced current
4. Always keep in mind that there are two
magnetic fields
a. An external field whose flux must be
changed if it is to induce an electric current
b. A magnetic field produced by the
induced current
21.2
S-139
A rectangular wire loop that has sides of 1.2 m spins
in a magnetic field so that it makes a complete
revolution every 2.4s. If the magnetic field that it
spins through has a field strength of 1.9T, how
many loops are required to
produce
a maximum potential
difference of 120V?
Electromagnetic Induction
21.3 EMF Induced in a Moving
Conductor
Faraday’s Law of Induction; Lenz’s Law
If the rod above is made to move at a velocity v
The area of the rod increases A 
xlxvtlvt
So the change in area is
Blv
B


A
t

B
The induce EMF is
 Blv
t
21.3
Faraday’s Law of Induction; Lenz’s Law
Sometimes called motional emf
True as long as components are mutually
perpendicular
21.3
S-139
A dog with a mass of 3.5 kg is floating in space. He
has 25.8x1018 extra electrons placed on him.
A. What is the charge on the dog?
B. The magnetic field of the earth at the point he is
floating is 7T. What is the force on the dog?
C. What is the net force on
the dog if his rocket
pack is thrusting him at
a constant 85 m/s
parallel to the magnetic
field?
Electromagnetic Induction
21.4 Changing Magnetic Flux
Produces an Electric Field
Changing Magnetic Flux Produces Electric Field
Since there is an induced current when there is
an induced EMF, there must be an electric
field
A changing magnetic field induces and electric
field
F  qvB
So since
And
qvB
F
EE vB
qq
The electric field must be
21.4
S-140
An alpha particle (2 protons, 2 neutrons) is shot
upward into a 5T magnetic field that is directed
into the plane of the board. It is traveling at
200,000 m/s when it enters the field.
A. What is the force on the particle?
B. What is the
diameter of the arc
that it travels
through?
Electromagnetic Induction
21.5 Electric Generators
Electric Generators
Generator – converts mechanical energy
(spinning) into AC current.
Generator Simulation
If we look at just one perpendicular arm of the
loop
  Blv sin q
Since we have two arms in each loop
  2Blv sin q
Now if we add loops
  2NBlv sin q
21.5
S-141
A 250 kg fat dude is standing on a slope that
makes an angle of 52o with the horizontal.
If the coefficient of
friction is 0.22, what
is his acceleration
down the slope?
Funny
S-142
A electron is accelerated through 10V and
then injected perpendicular to a 25T field
pointed downward. What is the centripetal
force acting on the electron?
S-143
Happy Test Day