We learned that current carrying wires produce a magnetic field around them.
The reverse is also true. A changing magnetic field can induce a current in a wire.
The current is called an induced current because it comes about (is induced) by the changing magnetic field.
Chapter 19: Magnetism
1

If we hold a magnet near a coil of wire nothing happens.
If we now move the magnet towards or away from the coil, a voltage and current is induced.
Let’s see if we can see what is going on together.
But I will need a helper,
And you will have to make some predictions first.
LoggerPro with Coil
Link to Solutions
Chapter 19: Magnetism
When the magnet moves towards the coil the magnetic field through the coil increases, inducing a current.
When it is moved away, the field decreases, creating a current, but in the opposite direction.
Chapter 19: Magnetism
2

The changing magnetic field causes an induced current. Since a source of emf (voltage) is needed to produce a current (remember
Ohm’s Law), the moving magnet acts like a source of emf . So we would say the moving magnet induces an emf in the coil, producing an induced current .
Chapter 19: Magnetism
Another way to describe this induced emf is in terms of something called magnetic flux .
Magnetic flux [

B
] is similar to the luminous flux or electric flux. It is deals with the magnetic field and the surface through which it passes. It is a measure of the quantity of magnetism.
Magnetic flux [

B
] is mathematically the dot product of the Magnetic Field [B] and the enclosed area [A] you are measuring the flux through

B
= B · A = (B)(A perp
)
Chapter 19: Magnetism
3

The flux only depends on the portion of the magnetic field that is perpendicular to the area in which is passes through. So when the magnetic field direction is not perpendicular to the area the equation for flux becomes

B

BA cos

Chapter 19: Magnetism
So, an emf [ E ] is created due to the rate change of flux [

]. How can the flux change?
• the coil can spin (

)
• The coil can change area (

A )
• The coil can move out of the field
• The magnetic field can change strength (

B )
Since flux depends on B , A and

, that means that any of them can be changing to produced an induced emf E .
Chapter 19: Magnetism
4

Michael Faraday discovered electromagnetic induction. He discovered that whenever there is a change in flux through a coil of wire, an emf is produced.
This equation is one of the most important law corresponding to modern day electrical power as it is the basis for all electric generators.
  
 t

 t

0
0
 

 t
Chapter 19: Magnetism
Often a magnetic flux passes through a coil of wire consisting of more than one loop. Each loop abides by the previous equation for the emf produced.
So if a coil has N loops, we get
  
N


 t

 t

0
0


 
N

 t
Faraday’s Law of Electromagnetic Induction w/loops
Let’s see some examples
Chapter 19: Magnetism
5

The induced emf creates an induced current through the loop. Conventional current runs out of the positive terminal and into the negative. So which is positive and which is negative? Which direction does the current flow?
Chapter 19: Magnetism
As it turns out,
The induced current will create its own magnetic field called the induced magnetic field.
The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.
Or the induced magnetic field opposes the change in the original magnetic flux, so the direction of the current must address this.
This is known as Lenz’s Law, and is why that negative sign is on Faraday’s Law of Induction – The induced emf opposes the change in flux.
Chapter 19: Magnetism
6

1.
Determine whether the flux is increasing or decreasing.
2.
Find out what direction the induced magnetic field must be to oppose this change.
• If the flux is increasing, the induced field must be opposite the direction of the original field
• If the flux is decreasing, the induced field must be in the same direction as the original field
3.
Use the RHR-2 to determine what direction of current will result in an induced field that is in this direction.
Chapter 19: Magnetism
Moving magnet through a coil.
The B-field is increasing, so flux is increasing.
The induced field must be opposite the direction of the original field
Induced current is as shown.
Chapter 19: Magnetism
7

The magnet does not have to move, but there does have to be relative motion between the wire circuit and a magnetic field.
Another way to do this is to move a conductor in a magnetic field.
Chapter 19: Magnetism
When the bar moves through the field, a force is applied on the electrons in it. In this case the force points ...
UP 
This magnetic force separates the charges according to
F
 q
 v
Chapter 19: Magnetism

B
8

The mobile electrons move to the bottom, leaving a positive charge at the top.
This charge difference now creates an attractive electric force which competes against the magnetic force.
The separation stops when the electric force balances with the magnetic force.
But the separated charges now have a potential difference associated with them.
Derive what’s happening
Chapter 19: Magnetism
We can see that the motional emf [ E ] is defined
E = ν B L
Where E is the emf,
ν is the velocity of the bar,
B is the magnetic field strength, and L is the length of the conductor bar.
As you can see, E = 0 when
ν
= 0, and as
ν increases, so does E .
Is this really the same as Faraday’s Law ?
Chapter 19: Magnetism
9

An electric generator transforms mechanical energy into electrical energy. That is, it generates electricity.
Chapter 19: Magnetism
Chapter 19: Magnetism
10

My never dying flashlight
Chapter 19: Magnetism
Electric Guitar Pickups
Chapter 19: Magnetism
11

Moving coil microphone
Chapter 19: Magnetism
Chapter 19: Magnetism
12

An eddy current is a swirling current set up in a conductor in response to a changing magnetic field. By
Lenz's law, the swirling current sets up a magnetic field opposing the change. In a conductor, electrons swirl in a plane perpendicular to the magnetic field.
Eddy currents cause energy to be lost. More accurately, eddy currents transform more useful forms of energy, such as kinetic energy, into heat, which is generally much less useful. In many applications the loss of useful energy is not particularly desirable, but there are some practical applications such as train brakes.
Chapter 19: Magnetism
Eddy Current Application: train brakes
Draw a set of pictures for the green region, to show the direction of the induced current in the green region as it enters the magnetic field.
What is the direction of the force induced?
Chapter 19: Magnetism
13

Chapter 19: Magnetism
14