Chapter 23
Induced Emf’s
Induced emf

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
Faraday’s Experiment




The purpose of the secondary circuit is to
detect current that might be produced by
the magnetic field
When the switch is closed, the ammeter
deflects in one direction and then returns
to zero
When the switch is opened, the ammeter
deflects in the opposite direction and then
returns to zero
When there is a steady current in the
primary circuit, the ammeter reads zero
Faraday’s Conclusions



An electrical current is produced by a
changing magnetic field
The secondary circuit acts as if a
source of emf were connected to it
for a short time
It is customary to say that an
induced emf is produced in the
secondary circuit by the changing
magnetic field
INDUCTION
Michael Faraday (1791 – 1867)
…it appeared very extraordinary, that as every
electric current was accompanied by a corresponding
intensity of magnetic action at right angles to the current,
good conductors of electricity, when placed within the
sphere of this action, should not have any current induced
through them, or some sensible effect produced equivalent
in force to such a current.
Primary Coil
Secondary coil
G
?
Summary of Experimental Findings
EMF is induced in the secondary coil
Only when the magnetic field through it changes.
EMF induced is bigger if the area of coil is bigger.
EMF is induced always in the opposite direction of
change in magnetic field.
Vind = - A (dB/dt)
= - d/dt
 = A B : magnetic flux
Magnetic Flux


The emf is actually induced by a
change in the quantity called the
magnetic flux rather than simply by
a change in the magnetic field
Magnetic flux is proportional to both
the strength of the magnetic field
passing through the plane of a loop
of wire and the area of the loop
B
 = A B┴
A
= (0.3 x 0.2)(0.175 sin(40))
= 0.06 x 0.112
= 0.0067 T.m2
B = 0.175 T
B┴
B
40
B//
0.3 m
+
+
+
+
-
Vind = - d/dt
Vt = -3 d/dt
Net number of loops
Example 23.2
150 turn loop with a 0.75 cm2 cross-section
Magnetic field: 0 T  0.25 T in 3.6 s
5 Ohm
What is the induced current in the coil?
Faraday’s Law and
Electromagnetic Induction


The instantaneous emf induced in a
circuit equals the time rate of change of
magnetic flux through the circuit
If a circuit contains N tightly wound
loops and the flux changes by dΦ
during a time interval dt, the average
emf induced is given by Faraday’s Law:
d B
  N
dt
Faraday’s Law and Lenz’ Law

The change in the flux, dΦ, can be produced
by a change in B, A or θ
• Since ΦB = B A sin θ

The negative sign in Faraday’s Law is
included to indicate the polarity of the
induced emf, which is found by Lenz’ Law
• The polarity of the induced emf is such that it
produces a current whose magnetic field opposes
the change in magnetic flux through the loop
• That is, the induced current tends to maintain the
original flux through the circuit
Applications of Faraday’s Law –
Ground Fault Interrupters

The ground fault
interrupter (GFI) is a
safety device that
protects against
electrical shock
• Wire 1 leads from the wall
outlet to the appliance
• Wire 2 leads from the
appliance back to the wall
outlet
• The iron ring confines the
magnetic field, which is
generally 0
• If a leakage occurs, the
field is no longer 0 and the
induced voltage triggers a
circuit breaker shutting off
the current
Applications of Faraday’s Law –
Electric Guitar




A vibrating string
induces an emf in a coil
A permanent magnet
inside the coil
magnetizes a portion of
the string nearest the
coil
As the string vibrates at
some frequency, its
magnetized segment
produces a changing
flux through the pickup
coil
The changing flux
produces an induced
emf that is fed to an
Motional EMF
FE = -eE
x
-
FB = -evB
B
-
x
x
x
x
x
x
x-
x
x
x
-
x
x -
x
x
x
x
-
E
-
x
x
x
x
x
x
x
x
x
x
x
x
x
v
eE = evB
E = vB
Vind = LE = LvB