Lecture 16
Chapter 33
Physics II
07.28.2015
Faraday’s Law
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture Capture:
http://echo360.uml.edu/danylov201415/physics2spring.html
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Motional EMF
Consider a conductor of length l that moves with velocity v through a perpendicular
magnetic field B.
B
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Motional EMF
(downward, -y direction)
Let’s calculate the potential difference between ends:
∙
∙
It is called the motional EMF
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Example:
A plane flies in the Earth’s magnetic field (B = 5x10-5T)
with v=1000 km/h; l=70m (between the wings)
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(not very significant to consider)
Department of Physics and Applied Physics
ConcepTest 3

Motional EMF 2
A metal bar moves through a magnetic field.
The induced charges on the bar are:
So the magnetic force qvB on a positive charge is to the left,
so positive charge will be accumulated near the left side of the bar,
ConcepTest 2

Motional EMF 1
A metal bar moves through a magnetic
field. The induced charges on the bar are:
∥
So the magnetic force is zero and there is no charge separation,
no motional EMF
Induced current in a circuit (rod moving to the right)
Consider a conducting rod sliding on a U-shaped conducting rail. So here we completed a
circuit and drove an electric current. B is perpendicular to the plane of the rail.
The EMF induced in the rod is:
The induced current flows
through the moving rod
I
This current I in B will experience a
magnetic force to the left:
So, in order to keep the wire moving at a
constant speed v, we would need to apply
a pulling force to the right.
I
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Induced current in a circuit (rod moving to the left)
The figure shows a conducting wire sliding to the left (changed direction).
This induced current I in B will experience a
magnetic force to the right:
I
So, in order to keep the wire moving at a
constant speed v, we would need to apply
a pulling force to the left.
I
How can this device be called?
A device that converts mechanical energy
to electric energy is called a generator.
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ConcepTest 4
Electrical generator
A) up

An induced current flows clockwise
as the metal bar is pushed to the
right. The magnetic field points
B) down
C) Into the screen
D) Out of the screen
E) To the right
Magnetic Flux
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The Area Vector
 Let’s define an area vector
to be a vector in
the direction of, perpendicular to the surface, with a
magnitude A equal to the area of the surface.
 Vector
has units of m2.
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Slide 33-44
The Basic Definition of Flux (of air)
 Imagine holding a rectangular wire loop of area A = ab in front of a fan.
 The volume of air flowing through the
loop each second depends on the angle
between the loop and the direction of
flow.
 No air goes through the same loop if it lies parallel to the flow.
 The flow is maximum through a loop that is perpendicular to the airflow.
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Magnetic Flux
The magnetic flux measures the amount
of magnetic field passing through a loop
of area A if the loop is tilted at an angle
 from the field:
θ
In the case when magnetic field is not uniform and a surface is not
flat, than the magnetic flux is
⋅
The SI unit of magnetic flux is the weber:
1 weber = 1 Wb = 1 T m2
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Example: Determining flux
A square loop of wire encloses area A1.
A uniform magnetic field B perpendicular to
the loop extends over the area A2.
What is the magnetic flux through the loop A1?
0
⋅
Area A1
⋅
Area A1 -A2
⋅
A2
Area A2
∥
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A2
ConcepTest 1

Electrical generator
The metal loop is being pulled
through a uniform magnetic field.
Is the magnetic flux through
the loop changing?
B=const
A=const
Theta=const,
So the flux is const
A) yes
B) no
ConcepTest 2

Electrical generator II
The metal loop is rotating
in a uniform magnetic field. Is the
magnetic flux through the loop
changing?
B=const
A=const
Theta=changes,
So the flux is NOT const
A) yes
B) no
Faraday’s Law
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Recall Faraday’s experiment
We saw in the previous class that a moving magnet through the
loop can cause an induced current. How can it be explained?
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Faraday’s Law
Now with the definition of flux, we can write mathematically
what Faraday saw experimentally
Faraday’s law of induction: the emf induced in a circuit is equal to the rate of
change of magnetic flux through the circuit:
So we can induce EMF by changing: B, θ, A:
Spinning a loop
θ
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a loop is shrunk
Lenz’s Law
The minus sign gives the direction of the induced emf.
To avoid dealing with this minus, we will calculate EMF in two steps:
1)
2) Apply Lenz’s Law
i.e. “Any system doesn’t like changes”
It opposes to a growing flux
And
Supports a dying flux
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Lenz’s Law (example)
 Pushing the bar magnet into the loop
causes the magnetic flux to increase
in the upward direction.
 To oppose the change in flux, which is
what Lenz’s law requires, the loop
itself needs to generate
an downward-pointing magnetic field.
 The induced current ceases as soon as
the magnet stops moving.
has CW direction
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Example (Lenz’s Law)
The current in the straight wire is decreasing.
I
has CW direction
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ConcepTest 3

The current in the
straight wire is increasing.
Which is true?
Lenz’s law
A) There is a clockwise induced current
in the loop.
B) There is a counterclockwise induced
current in the loop C) There is no induced current in the loop.
1. The wire’s B field is into the screen and
increasing.
2. To oppose the increase in flux, the field of the
induced current must point out of the screen.
3. From the right-hand rule, an inward field
needs a ccw current.
has CCW direction
ConcepTest 4 Loop and Wire II
What is the induced current if
1) clockwise
the wire loop moves in the
2) counterclockwise
direction of the yellow arrow?
3) no induced current
The magnetic flux through the loop
is not changing as it moves parallel
to the wire. Therefore, there is no
induced current.
I
Faraday’s Law for a U-shaped rail/rod system
Let’s apply Faraday’s law for a conducting rod sliding on a U-shaped conducting rail.
B is perpendicular to the plane of the rail.
We can find the induced emf and current by using Faraday’s law and Ohm’s law:
The EMF induced in the loop is:
The induced current flows
through the loop:
Direction of the induced current:
has CCW direction
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ConcepTest 4
Faraday’s Law
A) 200 V

The induced emf around this
loop is
B) 20 V
C) 2 V
D) 0.5 V
E) 0.2 V
What you should read
Chapter 33 (Knight)
Sections
 33.3
 33.4
 33.5
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Thank you
See you tomorrow
95.144, Summer 2015, Lecture 16
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