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Today’s agenda:
Induced emf.
You must understand how changing magnetic flux can induce an emf, and be able to
determine the direction of the induced emf.
Faraday’s Law.
You must be able to use Faraday’s Law to calculate the emf induced in a circuit.
Lenz’s Law.
You must be able to use Lenz’s Law to determine the direction induced current, and
therefore induced emf.
Generators.
You must understand how generators work, and use Faraday’s Law to calculate numerical
values of parameters associated with generators.
Back emf.
You must be able to use Lenz’s law to explain back emf.
We can quantify the induced emf described qualitatively in the
previous section of this lecture by using magnetic flux.
Experimentally, if the flux through N loops of wire changes by
dB in a time dt, the induced emf is
dB
ε = -N
.
dt
*Faraday’s Law of
Magnetic Induction
ε average = - N
B
.
t
Faraday’s law of induction is one of the fundamental laws of
electricity and magnetism.
I wonder why the – sign…
Your text, page 959 of the 14th edition, shows how to determine the direction of the induced emf. Argh!
Lenz’s Law, coming soon, is much easier.
*Well, one expression of Faraday’s Law
In the equation
ε = -N
dB
,
dt
Faraday’s Law of
Magnetic Induction
 B   B  dA is the magnetic flux.
This is another expression of Faraday’s Law:
dB
 E  ds = - dt
We’ll use this version
in the next lecture.
The fine print, put here for me to ponder, and not for students to worry about. A magnetic force does no work on a moving (or stationary) charged particle. Therefore the magnetic force
cannot change a charged particle’s potential energy or electric potential. But electric fields can do work. This equation shows that a changing magnetic flux induces an electric field,
which can change a charged particle’s potential energy. This induced electric field is responsible for induced emf. During this lecture, we are mostly going to examine how a changing
magnetic flux induces emf, without concerning ourselves with the “middleman” induced electric field.
Example: move a magnet towards a coil of wire.
N=5 turns
A=0.002 m2
dB
= 0.4 T/s
dt
I
d B  dA
dB
ε = -N
= -N
dt
dt
d BA 
ε = -N
dt
N
+
S
v
-
(what assumptions did I make here?)
dB
ε = -NA
dt
T
ε = - 5  0.002 m2   0.4  = -0.004 V

s
Ways to induce an emf:
 change B
Possible homework hint:  B   d B   B  dA   B(t) dA if B varies but loop  B.
 change the area of the loop in the field
Possible homework hint: for a circular loop, C=2R, so A=r2=(C/2)2=C2/4, so you can express d(BA)/dt in terms of dC/dt.
Ways to induce an emf (continued):
 changing current changes B through conducting loop
a
I
B
b
Possible Homework Hint.
The magnetic field is not uniform through the loop, so you
can’t use BA to calculate the flux. Take an infinitesimally thin
strip. Then the flux is d = BdAstrip. Integrate from a to b to
get the flux through the strip.
Ways to induce an emf (continued):
 change the orientation of the loop in the field
=90
=45
=0