Electromagnetic Induction
Basic Concepts
Faraday’s Law (changing magnetic flux
induces emf)
Lenz’s Law (direction of induced current)
Motional emf
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Two Experiments
• Experiment 1: Conducting Coil and Magnet
• Experiment 2: Pair of Conducting Coils
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Two Experiments
Induced current and induced emf when something changes.
What is it?
Faraday:
An emf is induced in the coil when the number of magnetic field
lines that pass through the coil is changing.
How to determine the amount of magnetic field lines that pass
through a coil?
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Faraday’s Law of Induction
The emf induced in a circuit is directly proportional to the
time rate of change of the magnetic flux through the circuit:
dB
 
dt
If the circuit contains N loops all with the same area an emf is
induced in every loop, and the total induced emf is
dB
 N
dt
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Ways to Change the Magnetic Flux
dB
 
dt
     
     
      B
     
     
dB
 N
dt
• Change the magnetic field within the coil
• Change the area of the coil in the field (for
example, stretch the coil or move it in or out of the
field)
• Change the angle between the magnetic field
direction and the coil (rotate the coil)
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Some Applications of Faraday’s Law
•
•
•
•
•
•
Ground Fault Interruptors (GFI)
Electric Guitar Pickup Coils
Alternators
Generators
Phonograph Cartridges
Magnetic Tape Readers
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Direction of Induced emf
dB
 N
dt
What about that pesky minus sign?
An induced emf produces a current that creates a magnetic
flux to oppose the original change in the magnetic flux.
This is known as Lenz’s Law
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Examples of Lenz’s Law
Determine the direction of the induced current in each resistor below.
1.
I
I
3.
2.
I
I suddenly decreases.
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Motional emf
Motional emf is the emf induced in a conductor moving in a
magnetic field. We will limit this to constant magnetic fields.
     The magnetic force on the electrons in the
+
     bar causes them to move downward.
E

 v  B
l
FB  qv  B   ev  B
    
    
This separates the charges in the bar producing an electric field in
the bar. The electric field exerts an upward force on the electrons.
FE  qE   eE At equilibrium the forces balance, and
FB  FE  0  e E  evB
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Motional emf
    
+
    
E

 v  B
l
    
    
The separation of charges also produces a
voltage difference across the bar, or an
induced emf, .
  El
Since
e E  evB
we can write
El  Blv or   Blv
When a conductor moves through a uniform magnetic field a
potential difference is maintained between the ends of the
conductor.
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Motional emf
l R
         
      v  
        F
ap
        p 
 I        
         
B
x
A more interesting situation occurs when the moving bar is part of a
closed conducting path. We assume the bar has zero resistance, and
that the stationary part of the circuit has resistance R. As the bar is
pulled to the right with velocity v by the applied force Fapp the
electrons are again subject to a downward force. Now, however,
the electrons are free to move in the closed conducting path and a
counterclockwise current is established.
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Motional emf
l R
         
      v  
        F
ap
        p 
 I        
         
B
x
Does the induced counterclockwise current follow Lenz’s law?
As the bar slides to the right the magnetic flux through the
circuit into the page is increasing. Lenz’s law says the induced
current will produce a magnetic field to oppose that increase.
In other words, the induced current should produce a magnetic
field that points out of the page. A counterclockwise current
does this.
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Motional emf
l R
         
      v  
        F
ap
        p 
 I        
         
B
x
The magnetic flux through the circuit at this instant is B = BA = Blx.
So Faraday’s law gives the following:
dB
d
dx
 
   Blx    Bl
  Blv
dt
dt
dt
Hence

Blv
I 
R
R
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Motional emf
l R
         
      v  
 F       F
B
ap
        p 
 I        
         
B
x
As the bar moves through the uniform magnetic field B it also
experiences a magnetic force FB.
FB  Il  B
This force is opposite the applied force and because the bar moves
with constant velocity it must be equal in magnitude as well.
Fapp  FB  IlB
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Motional emf
l R
         
      v  
 F       F
B
ap
        p 
 I        
         
Fapp  FB  IlB
B
x
The power supplied by the applied force is then P  Fappv   IlB  v
Blv
Since we found I 
then P   IlB  v  I  Blv   I 2 R
R
First the mechanical energy is converted to electrical energy. This
electrical energy is then converted to internal energy in the resistor.
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