AP Physics
Chapter 20
Electromagnetic Induction
Chapter 20: Electromagnetic Induction
20.1: Induced Emf’s: Faraday’s Law and Lenz’s
Law
20.2-4: Omitted
Homework for Chapter 20
• Read Chapter 20
• HW 20: p.658-660: 3,5,6,8,9,10,11,13,14,18,21-24.
20.1 Induced Emf’s : Faraday’s Law
and Lenz’s Law
It is more like an electromagnet, because the
movements of the metal liquids create
electrical currents which change in strength
and direction.
• As we saw in Chapter 19, electric current produces a magnetic field. On the
flip side, changing magnetic fields can be used to produce electric current.
electromagnetic induction
- The process of generating a current
through a circuit due to the relative motion between a wire and a magnetic
field when the wire is moved through the magnetic field or the magnetic field
moves past the wire.
• When there is no relative motion between
the magnet and the loop, the number of field
lines (in the diagram, 7) through the loop is
constant.
• The galvanometer (measuring current)
shows no deflection.
• Moving the magnet toward the loop
increases the number of field lines now
passing through the loop (now 12).
• An induced current is detected by the
galvanometer.
• Moving the magnet away from the loop
decreases the number of field lines passing
through the loop (now 5).
• The induced current is in the opposite
direction as indicated by the opposite
needle deflection.
• The induced current can also occur if the loop is moved toward or away from a
stationary magnet.
• The magnitude of the induced current depends on the speed of that relative
motion.
Exception: When a loop is moved
parallel to a uniform magnetic field,
there is no change in the number of
field lines passing through the loop
and no induced current.
• Another way to induce a current in a
stationary loop of wire is to vary the current in
another loop close to it.
• When the switch is closing in the right-loop
circuit, the current buildup (typically over a
few milliseconds) produces a changing
magnetic field that passes through the other
loop, inducing a current in it.
• When the switch is opened the
magnetic field lines through the lefthand loop decreases.
• The induced current in this loop is
then in the opposite direction.
• The current induced in a loop is caused by an induced electromotive force (emf)
due to electromagnetic induction.
• An emf represents energy capable of moving charges around a circuit. We
previously studied batteries as a chemical source of emf.
• A moving magnet can create an induced emf
causes current.
in a stationary loop, which
• In the case of two stationary loops, where a changing current in one circuit
induces an emf in the other, we call it mutual induction
. .
Micheal Faraday
(1791-1867)
• Micheal Faraday and Joseph Henry conducted independent experiments on
electromagnetic induction around 1830.
• Faraday drew the conclusion:
An induced emf is produced in a loop by changing the number of
magnetic field lines passing through the plane of the loop.
magnetic flux
() – a measure of the number
of field lines passing through and area (A). The variable
we use to represent magnetic flux is capital phi.
a) The area can be represented by a vector A
perpendicular to the plane of the area.
b) When the plane of a rotating loop is perpendicular to
the field and  = 0°, then  = max = BA.
c) When  = 180°, the magnetic flux has the same
magnitude but is opposite in direction:  = - max = - BA.
d) When and  = 90°, then  = 0.
e) As the loop is rotated from an orientation perpendicular to the field to one more
nearly parallel to the field, less area is open to the field lines and the flux
decreases. In general,  = BA cos .
Side View
m = BA cos 
where
magnetic flux
On Gold
Sheet
B is the magnetic field
A is the area of the loop
 is the angle between B and A
• The unit of magnetic flux is the weber (Wb). 1 Wb = 1 T·m2
• If the coil has N number of turns, then the total flux through the coil is the sum of
the flux through each turn. Hence,
m = NBA cos 
magnetic flux through a solenoid
Example 20.1: A circular loop of radius 0.20 m is rotating in a uniform magnetic
field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop
and the magnetic field vector are (a) parallel, (b) perpendicular, (c) at 60°.
Examples: pacemakers stopping, migrating birds get lost, GPS
won’t work, etc.
(average for the
time interval t)
For N loops of wire, Faraday’s Law of
Induction can be written:
 = - N  m
t
• In other words, Lenz’s Law states that
the direction of the induced current
opposes the increase in flux.
Example A:
Example B:
Example C:
On Gold
Sheet
The polarity of induced emf is given by
the right hand force rule. Therefore, the
force on the electrons would be down.
• The magnitude of the induced emf is called motional emf.
.
+
-
Example 20.2: A coil is wrapped with 100 turns of wire on a square frame with sides
18 cm. A magnetic field is applied perpendicular to the plane of the coil. If the field
changes uniformly from 0 to 0.50 T in 8.0 s, find the average value of the
magnitude of the induced emf.
Example 20.3: A square coil of wire with 15 turns and an area of 0.40 m2 is placed
parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular
to the magnetic field in 0.050 s. What is the magnitude of the average induced emf?
Example 20.4: An airplane with a wing span of 50 m flies horizontally with a speed
of 200 m/s above the Earth at a location where the downward component of the
Earth’s magnetic field is 6.0 x 10-5 T. Find the magnitude of the induced emf
between the tips of the wing.
right to left through
left to right through the
left to right through the resistor.
right to left through the resistor.
Check for Understanding
1. The unit of magnetic flux is
a) Wb
b) T·m2
c) T·m / A
d) both a and b
Answer: d
2. Magnetic flux through a loop can change due to a change in
a) the area of the coil
b) the magnetic field strength
c) the orientation of the loop
d) all of the above
Answer: d
Check for Understanding
3. For an induced current to appear in a loop of wire,
a) there must be a large magnetic flux through the loop
b) the loop must be parallel to the magnetic field
c) the loop must be perpendicular to the magnetic field
d) the magnetic flux through the loop must vary with time
Answer: d
Homework for Chapter 20
• Read Chapter 20
• HW 20: p.658-660: 3,5,6,8,9,10,11,13,14,18,21-24.
Chapter 20 Formulas
m = NBA cos 
 = - N  m
t
 = BLv
magnetic flux
N is the number of loops
B is the magnetic field
A is the area of the loop
 is the angle between B and A
average induced emf
N is the number of loops
 m is the final minus initial magnetic flux
 t is the final minus initial time
induced motional emf
B is the magnetic field
L is the length of the conductor
v is the speed of the conductor