Lecture 16
Chapter 33
Physics II
03.27.2015
Faraday’s Law
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
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http://echo360.uml.edu/danylov201415/physics2spring.html
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
Magnetic Flux
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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.
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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.
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
∥
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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?
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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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Department of Physics and Applied Physics
Example (Lenz’s Law)
The current in the straight wire is decreasing.
I
has CW direction
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Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
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
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics
Thank you
See you on Tuesday
95.144, Spring 2015, Lecture 16
Department of Physics and Applied Physics