2. Faraday’s Experiment – Set Up
●A current can be produced by a changing
magnetic field
○ First shown in an experiment by Michael Faraday
■ A primary coil is connected to a battery
■ A secondary coil is connected to an ammeter
3. Faraday’s Experiment-Results
1. The switch is closed, the ammeter reads a current and then
returns to zero
2. The switch is opened, the ammeter reads a current in the
opposite direction and then returns to zero
3. When there is a steady current in the primary circuit, the
ammeter reads zero
● An (Induced EMF) electrical current is produced by a changing
magnetic field
● The emf is actually induced by a change in the magnetic flux
rather than simply by a change in the magnetic field
4. Magnetic Flux
●A loop of wire is in a uniform
magnetic field B
●The loop has an area A
●The flux is defined as
○ΦB
= B
A = B A cos θ
■ θ is the angle between B and
the normal to the plane
○SI units of flux are T· m² =
Wb (Weber)
5. Electromagnetic Induction –
An Experiment
● A magnet moves toward a loop of
wire, the ammeter shows the
presence of a current (a)
● The magnet is held stationary, there is
no current (b)
● The magnet moves away from the
loop, the ammeter shows a current in
the opposite direction (c)
● If the loop is moved instead of the
magnet, a current is also detected
6. Faraday’s Law and
Electromagnetic Induction
●If a circuit contains N tightly wound loops and
the flux changes by ΔΦB
during a time
interval Δt, the average emf induced is given
by Faraday’s Law:
●The change in the flux, ΔΦB
, can be
produced by a change in B, A or θ
○Since ΦB
= B A cos θ
EMF = -N ΔΦB
t
7. Lenz’ Law – Moving Magnet
Example
● A bar magnet is moved to the right toward a
stationary loop of wire (a)
○ As the magnet moves, the magnetic flux
increases with time
● The induced current produces a flux to the
left, so the current is in the direction shown
(b)
● The current caused by the induced emf
travels in the direction that creates a
magnetic field opposing the change in the
original flux through the circuit
8. Application of Faraday’s Law –
Motional emf
● A straight conductor of length ℓ
moves perpendicularly with
constant velocity through a
uniform field
● The charges in the conductor
experience a magnetic force
○ F = q v B
● The electrons tend to move to
the lower end of the conductor
9. Motional emf, cont
●The potential difference between the ends of the
conductor can be found by
○ Emf = V = B ℓ v
○ The end with “+” is at a higher potential
●A potential difference is maintained across the
conductor as long as there is motion through the
field
○ If the motion is reversed, the polarity of the potential
difference is also reversed
10. Motional emf in a Circuit
●As the bar is pulled to the
right with a given velocity
under the influence of an
applied force, the free
charges experience a
magnetic force along the
length of the bar
●This force sets up an
induced current because
the charges are free to
move in the closed path
11. Motional emf in a Circuit, cont
● The changing magnetic flux
through the loop and the
corresponding induced emf in
the bar result from the
change in area of the loop
● The induced, motional emf,
acts like a battery in the
circuit
12. Lenz’ Law Revisited – Moving
Bar Example
●The flux due to the
external field is increasing
into the page (since area
is increasing)
●The flux due to the
induced current must be
out of the page
●Therefore the current
must be counterclockwise
when the bar moves to
the right
13. Lenz’ Law, Bar Example, final
● The bar is moving toward
the left
● The magnetic flux through
the loop is decreasing with
time (since area is
decreasing)
● The induced current must
be clockwise to to produce
its own flux into the page
14. Problems
32.16 A solenoid 60 cm long has 5000 turns on it and is wound on an iron rod of 0.75 cm
radius. Find the flux through the solenoid when the current in it is 3.0 A. The relative
permeability of the iron is 300. Ans. 1.7 mWb
32.18 The flux through the solenoid of Problem 32.16 is reduced to a value of 1.0 mWb in a
time of 0.050 s. Find the induced emf in the solenoid. Ans. 67 V
32.19 A flat coil with radius 8.0 mm has 50 loops of wire. It is placed in a magnetic field B =
0.30 T in such a way that the maximum flux goes through it. Later, it is rotated in 0.020 s to
a position such that no flux goes through it. Find the average emf induced between the
terminals of the coil. Ans. 0.15 V
15. Problems
32.20 The square coil shown in Fig. 32-9 is 20 cm on a
side and has 15 loops of wire. It is moving to the right at
3.0 m/s. Find the induced emf (magnitude and direction) in it
(a) at the instant shown and (b) when the entire coil is in the
field region. The magnetic field is 0.40 T into the page.
Ans. (a) 3.6 V counterclockwise; (b) zero
32.21 The magnet in Fig. 32-10 rotates as shown on a pivot through its center. At the
instant shown, in what direction is the induced current flowing (a) in resistor AB (b) in
resistor CD? Ans. (a) B to A; (b) C to D
16. Problems
32.22 A train is moving directly south with a speed of 10 m/s. If the downward
vertical component of the Earth’s magnetic field is 0.54 G, compute the
magnitude and direction of the emf induced in a rail car axle 1.2 m long. Ans.
0.65 mV from west to east
32.24 How much charge will flow through a 200-Ω galvanometer connected to
a 400-Ω circular coil of 1000 turns wound on a wooden stick 2.0 cm in
diameter, if a magnetic field B = 0.0113 T parallel to the axis of the stick is
decreased suddenly to zero? Ans. 5.9 μC
