Chapter 22.6 Applications of Electromagnetic Induction to the Reproduction of
Sound.
When the strings of an electric guitar vibrates, an emf is induced in the coil of the
pickup. The two ends of the coil are connected to the input of an amplifier.
In a moving-coil microphone, sound waves cause the diaphragm to vibrate, and
this oscillating motion causes a wire voice coil to move back and forth through a
magnetic field, generating a current that varies in proportion to the original sound
wave. This varying current is transmitted through a wire lead to a transformer,
which converts it to a current that can be carried by wire cable to a recorder or
loudspeaker.
22.7 The Electric Generator
A electric generator consists of a coil of wire (conductor) that is rotated in a
magnetic field by some mechanical means. The current I arises because of the
magnetic force exerted on the charges in the moving conductor.
The magnitude if the motional emf developed in a conductor moving through a
magnetic field is given by:
ξ = vBL
To apply this to a generator we need to consider the velocity component v⊥ that
is perpendicular to B . Letting θ be the angle between v and B , it follows that
v⊥ = v sin θ , and the emf can be written as:
ξ = BLv⊥ = BLv sin θ
The emf produced is the same on both sides of the loop and the coil consists of
N loops:
ξ = N ( 2 BLv sin θ )
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ator.htm
emf induced in a rotating planer coil (alternator) aka AC generator.
ξ = NABω sin ωt = ξ o sin ωt
ω = 2π f
f = frequency in cycles per second or in the case of a generator revolutions per
second. To create 60 hertz ( 60Hz ) which is standard in America a generator must
rotate 60 times in one second. In Europe the standard is 50Hz and their
generators must rotate 50 times a second.
The Back Emf Generated by an Electric Motor
Consistent with lenz’s Law the induced emf ξ acts to oppose the applied emf V
and is called back emf or counter emf. The greater the speed of the motor the
greater the flux change through the coil and the greater the back emf.
I=
V −ξ
R
This is an application of Ohm’s Law I =
V
R
22.8 Mutual Inductance and Self-Inductance
The effect in which a changing current in one circuit induces an emf in another
circuit is called mutual induction. The induced ξ in the secondary coil is
proportional to the change in flux passing through it.
N s Φ s = MI P ⇒ M =
NsΦs
IP
M is mutual inductance
Substituting the equations into Faraday’s law, we find that:
ξs = − N s
∆ ( MI p )
∆ ( NsΦs )
∆Φ s
∆I
=−
=−
= −M P
∆t
∆t
∆t
∆t
ξs = −M
∆I P
∆t
ξ s emf due to mutual induction.
Self Inductance: The effect in which a changing current in a circuit induces an
emf in the same circuit is referred to as self induction
NΦ
I
Faraday’s law of induction now gives the induced emf as:
N Φ = LI ⇔ L =
ξ = −N
∆ ( NΦ)
∆ ( LI )
∆Φ
∆I
=−
=−
= −L
∆t
∆t
∆t
∆t
ξ = −L
∆I
∆t
ξ emf due to self induction.
The energy stored in an Inductor
The energy density in an Inductor
1 2
LI
2
energy
1 2
=
B
volume 2 µ0
Energy =
22.9 Transformers
A transformer is a device for increasing or decreasing an AC Voltage:
Equations for transformers:
Vs N s
=
Vp N p
A transformer that steps up the voltage simultaneously steps down the current,
and a transformer that steps down the voltage steps up the current. PP = PS
P=IV therefore I PVP = I SVS or
I S VP N P
=
=
I P VS N S