
ELECTROMAGNETIC
INDUCTION (Chapter 29)
INDUCTANCE
(Chapter 30) below
KEY
TERMS: induced current, induced emf, Faraday's law of induction, Lenz's
law, motional emf, induced electric field, Maxwell's equations.


Fig.
29.1 Induction of a current in a coil of wire



Whenever
there is a change in the number of magnetic field lines passing
through a loop of wire a voltage (or emf) is generated (or induced)
in the loop of wire. This is how an electric generator works. The phenomenon
is known as electromagnetic induction and is explained by
Faraday's law of induction:
e
=  dF / dt
where
F is the magnetic flux given
by the closed integral of the dot product B 0
dA.

According
to Faraday's law,
if there is no change (with time)
in the number of lines of B field,
or magnetic flux,
through a closed loop(s)
there will be no induced,
or generated,
voltage set up in the loop(s).

Fig.
29.2 Coil in a uniform constant magnetic field




Fig.
29.3 Magnetic flux (F)



According
to Faraday's law, as the
strength of a magnetic field (B) passing through a loop of wire
increases, there
will be an increase in the number of magnetic field lines, and therefore
an induced voltage, or emf,
set up in the wire loop.
If
the strength decreases there will also
be an induced emf set up in the loop but with the opposite polarity.
Lenz's
law indicates the polarity
of the induced emf.

Fig.
29.5 Coil in an increasing magnetic field




Fig.
29.6 Changing magnetic flux induces current (recall I = V / R)




Fig.
29.8 Alternator (AC generator)


In
an AC electric generator, or alternator, the flux through the loops of
wire (wound on the armature) changes, and therefore according to Faraday's
law there will be an emf induced in the loops of wire.
This induced
emf causes a current to flow in the loops.


Fig.
29.10 DC generator


In
a DC generator the direction of the induced current in the loops must
be changed every onehalf
turn of the generator shaft. This is done with split rings on the rotating
armature contacting the
stationary "brushes" which are in turn connected to the wires
coming out of the generator.
There
is another way to see how a current is set up in the loop.
The electric force equation F = q v x B and the right
hand rule indicate there is a force on the charges (electrons) in the
purple bar that is moving with velocity v.


Fig.
29.11Slidewire generator
Because the magnetic flux (F) through
the loop is changing (increasing) there is an emf induced in the
loop in accordance with Faraday's law.




Fig.
29.12 Induced current (I) causes a force F = I L x
B to be exerted on the bar.
This force is in the direction opposite to the velocity v.




Fig.
29.13 Lenz's law describes the tendency of nature to resist
any
change in magnetic flux passing through a loop of wire.
Changes in flux can be canceled by inducing a magnetic field
in the appropriate direction.




Fig.
29.14 Induced currents caused by changes in magnetic flux




Fig.
29.15 (a) Induced emf in rod, (b) induced current in wire loop




Fig.
29.17 Solenoid with changing current.
The galvanometer G will record the presence of an induced emf in
the loop of wire
caused by the change in flux passing through the loop.




Fig.
29.19 Eddy currents




Fig.
29.20 Metal detector


Maxwell's
Equations (section 29.7) will be covered later in Chapter 32
"Electromagnetic Waves."
Maxwell's four equations
1. Gauss's Law for electric fields
2. Gauss's Law formagnetic fields,
3. Faraday's Law, and
4. Ampere's Law as modified by Maxwell
predict the existence of electromagnetic waves capable of propagating
through empty space at the speed of light, which is an electromagnetic
wave.






Fig.
29.31 Lenz's law




Fig.
29.33 Lenz's law (Exercise 29.17)




Fig.
29.34 Lenz's law (Exercise 29.18)




Fig.
29.37 Lenz's law (Exercise 29.21)




Fig.
29.39 Motional emf (Exercise 29.26)




Fig.
29.57 Inclined linear generator (Problem 29.77)


INDUCTANCE
(Chapter 30)
KEY
TERMS: inductor, magnetic energy density, RL circuit, time constant,
LC circuit, electrical oscillation, series RLC circuit.


Fig.
30.4 An inductor, simply a loop or loops of conducting wire.
A magnetic field is set up when current passes through the wire
loop.
The B field can be calculated using Ampere's Law or the Law
of Biot and Savart.




Fig. 30.6
Voltage across resistor (R) and inductor (L).
The voltage across the inductor is actually a back emf in accordance
with Lenz's Law.
As the current being pushed through the inductor (coil) is increased,
the flux (F) through the coil increases
and this results in an induced current in the opposite direction
to the original current.
ENERGY
IS DISSIPATED IN A RESISTOR
AND STORED IN AN INDUCTOR.




Fig.
30.11 RL circuit




Fig.
30.12 and 30.13: Current versus time in an RL circuit




Fig.
30.14 Oscillation of current in an LC circuit




Oscillation
of current in an LC circuit
From Physics, 4th Edition, by Halliday, Resnick, and
Krane, page 830,
John Wiley & Sons, Inc. New York, 1992.




Fig.
30.15 Oscillating LC circuit




Fig.
30.17 Series RLC circuit


© 2009 J. F. Becker


