Lesson 20 - Faraday's Law of Induction
I.
Faraday's Law of Magnetic Induction
A changing magnetic flux will induce an emf in a circuit that is directly
proportional to the time rate of change of magnetic flux through the circuit.
   dΦ B
dt
The electromotive force, , is defined as the work done by the electric force
moving 1.00 Coulomb charge around a closed path .
 
   E d s
Electromotive force is similar to voltage in definition. However, there are some
important differences.
II.
1.
The electrostatic force is a conservative force while the emf is due to a
non-conservative force.
2.
The work done around a closed path for electrostatics is zero. This is the
basis of Kirchhoff's Voltage Law. For the nonconservative electric force
created by magnetic induction, the work done around a closed path is not
zero.
Alternators And Generators
Consider a loop rotating at a constant angular frequency in a constant magnetic
field as shown below:


B
The magnetic flux penetrating the loop is given by
ΦB 
Although the area of the loop and the strength of the magnetic field are constant,
the angle between the two vectors is changing with respect to time as the loop
rotates. Using the kinematic equations for rotation about a fixed axis, we have
θ
ΦB 
Using Faraday's Law of Induction, we have
   dΦ B 
dt
By Ohm's Law, the induced current is therefore
I  
R

t
I
t
This sinusoidal current is called _____________________ ________________
III.
Lenz's Law
The direction of any magnetic induction effect is such as to oppose the cause of
the effect.
S
S
N

v
CASE A

v
N
CASE B
In the first case, we find that the magnetic flux ___________________ as we
move the magnet. Thus, the induced current must create a magnetic field that
_________________ the flux.
In the second case, we find that the magnetic flux ___________________ as we
move the magnet. Thus, the induced current must create a magnetic field that
_________________ the flux.
Interesting Applications:
1.
Gauss Gun
2.
Superconductivity For Levitation
3.
Electromagnetic Breaking And Eddy Currents
IV.
Self-Induction

R
A.
When the switch closes, current begins to flow and creates a magnetic flux
through the circuit.
By Faraday's Law, the _________________ ___________________
_____________________ induces an _______________ that
produces a current that ______________________ the ______________
in the ___________________. This is called self-induced emf.
B.
Self induced emf is extremely important for circuits involving coils since the
magnetic field inside the coil can be very large. Consider the circuit below
containing a coil:
Coil

R
The self-induced emf on the coil is given by Faraday's Law as

For a coil of constant geometry with N loops, the magnetic field is proportional to
the magnetic flux through a single loop.
B
Since the magnetic field is caused by the current flowing through the circuit, we
have
N B for single loop  I
Thus, we have
N B  L I
where N is the number of loops
L is called the inductance (proportionality constant)
B is the magnetic flux through a single loop
I is the current flowing through the coil
We can rewrite our equation above in order to define the inductance of a coil as
L
The units of inductance are ______________________.
We now have a way to determine the induced emf across the coil if we know the
current flowing through the coil.

This is an extremely important result as it states that the current through a coil
can not be changed instantaneously as the coil has energy stored in its
magnetic field!!
An electrical element that stores energy in a magnetic field is called an
____________________________
Circuit Element
and has the symbol _____________.
Current-Voltage (emf) Relationship