• Last chapter we saw that a current produces a magnetic field.
• In 1831 experiments by Michael Faraday and
Joseph Henry showed that a changing magnetic field could induce a current in a circuit.
Faraday’s setup.
Switch
+ _
Battery
Ammeter
0.0 mA

• The coil with the switch is connected to a battery.
(Primary coil)
• When current goes through a coil, it produces a magnetic field.
• The coils are wrapped around an iron ring to intensify the magnetic field.
• The secondary coil is hooked up to an ammeter.
This coil is not hooked up to a battery.

When the switch in the primary coil is closed, the ammeter reads a current in the secondary coil for a short moment, then returns to zero.
When the switch is opened, the ammeter momentarily measures a current in the opposite direction before returning to zero.
When there is a steady current in the primary coil, there is no current read by the ammeter.

• Conclusion: An electric current can be produced from a changing magnetic field.
• The current produced in the secondary coil occurs only for the instant the magnetic field through the secondary coil is changing.
• The secondary circuit behaves as though a source of emf (a battery) was connected to it for a short time.
• An induced emf is produced in the secondary circuit by the changing magnetic field.

emf – electric motive force, not really a force.
This is a source of electrical work/energy per unit charge.
work/charge = volt
Devices that increase the potential energy of circulating charges (batteries, generators) are sources of emf.
Think of emf as a voltage increase.

While the magnetic field inside the secondary coil was changing, the secondary coil acted as is it was connected to a battery.
The changing magnetic field induced an electric field in the secondary wire that caused the current to flow.

Changing magnetic fields induce electric fields.
A constant magnetic field can also induce an electric field. Example of this is an electric generator.
If the magnetic field is constant then what is changing?
The property that creates an electric field is the changing of the magnetic flux.

Magnetic flux is defined in the same way electric flux was defined earlier.
Magnetic flux through a loop, is proportional to the strength of the B-field passing through the plane of the loop and the area of the loop.
B
= B A cos
B cos is the component of the B-field that is perpendicular to the loop.
B side view of loop

• The value of the magnetic flux is proportional to the number of B-field lines passing through the loop.
•
B
= B A cos is maximized when = 0. This is when the B-field is perpendicular to the loop.
• see fig. 20.3 for maximizing/minimizing the flux
• see example 20.1

Consider a wire loop connected to an ammeter.
Moving a magnet towards the loop will induce a current in one direction.
When the magnet is stationary, there is no induced current.
Moving the magnet away from the loop induces a current in the opposite direction.
This is similar to the Faraday experiment shown earlier .

• An emf is induced in a cicuit when the through the circuit changes with time.
B
• The instantaneous emf induced in a circuit equals the negative rate of change of
B with respect to time.
• This is Faraday’s Law of magnetic induction.
N t
B

Lenz’s Law: The induced current travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit.
If the flux is increasing in one direction, the induced current will be in the direction so that its own magnetic flux will be in the direction opposite of the original flux.
Nature wants to keep the flux constant .

The induced magnetic flux does not have to be in the opposite direction of the original flux.
Fig. 20.5. The original flux is upwards. As the
B-field is reduced in strength, the flux is reduced. Lenz’s law will show that the induced current will be in the direction so that the induced B-field is in the upward direction.
work out example 20.2

• Ground fault interrupters, used to protect against short circuits
• Pickups on electric guitars, converts the vibrations of the strings to an electrical signal.

• Earlier we changed the B-field with time.
• Now we keep the field constant. Look at the emf induced in a conductor moving through a magnetic field.

1 st look at straight conductor of length (L) moving with constant velocity through a uniform B-field pointing into the page.
In this example the velocity is normal to B-field.
Force on the electrons (-) is F
B
= qvB downward
Free electrons build up on the lower end, leaving a net positive charge on the upper end. This produces an
E-field in the conductor.
Electrons keep moving until the magnetic force is balanced out by the electric force qE.
qE = qvB or E = vb

The potential difference across the conductor is given by V = E L so V = EL = BLv
The upper end of the conductor will be at a higher potential than the lower end.

Now the conductor is part of a closed loop.
See pictures on page 667.
Conducting bar of length L slides along two fixed parallel conducting rails. Let the stationary part of the loop have a resistance R. A uniform and constant
B-field is perpendicular to the plane of the loop.
As the bar is pulled to the right, a magnetic force acts on the free charges in the bar. Since the bar is part of a closed loop, an induced current circulates.

The change in
B and the induced current are produced from the change in area of the loop as the bar moves.
If bar moved a distance x in time t, the flux changes as
B
.
B
=B A = BL x
( A = L x) using Faraday’s Law with 1 loop (N = 1) and ignoring the direction for now x t
B BL t
BLv

We call this motional emf since it is produced from the motion of a conductor through a magnetic field.
if we want to find the induced current, we use the resistance of the circuit R.
V = IR I = V/R
BLv
I
R R gives the magnitude of the induces current.
Use Lenz’s Law and right hand rule to get direction.