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Electromagnetic Induction Ch. 29
Induction experiments
Faraday’s law
Lenz’s law
Motional electromotive force
Induced electric fields
Eddy currents
Displacement Current
C 2012 J. F. Becker
(sec. 29.1)
(sec. 29.2)
(sec. 29.3)
(sec. 29.4)
(sec. 29.5)
(sec. 29.6)
(sec. 29.7)
Learning Goals - we will learn: ch 29
• The experimental evidence that a changing
magnetic field induces an emf !
• How Faraday’s Law relates the induced emf
in a loop to the change in magnetic flux
through the loop.
• How a changing magnetic flux generates an
electric field that is very different from
that produced by an arrangement of
charges.
• Four fundamental equations completely
describe both electricity and magnetism.
Current induced in a coil.
When B is constant and
the shape, location, and
orientation of the coil
does not change, the
induced current is zero
in the coil.
Conducting loop in increasing B field.
Magnetic flux through an area.
Lenz’s Law
The induced emf (or
current) always tends
to oppose or cancel
the change that
caused it.
O
O
Lenz’s law
Faraday’s Law of Induction
How electric generators, credit card readers, and
transformers work.
Eqn 29.3
A changing magnetic flux causes
(induces) an emf in a conducting loop.
C 2004 Pearson Education / Addison Wesley
Changing magnetic flux through a wire loop.
f = 90o
Alternator (AC generator)
f = 90o
DC generator
Slidewire generator
Magnetic force (F = IL x B) due to the induced current
is toward the left, opposite to velocity v.
Lenz’s Law
The induced emf (or
current) always tends
to oppose or cancel
the change that
caused it.
O
O
Lenz’s law
Currents (I) induced in a wire loop.
Motional induced emf (e):
e=vBL
because the potential
difference between a and b is
e = DV = energy / charge = W/q
e = DV = work / charge
DV = F x distance / q
DV = (q v B) L / q
so
e=vBL
Length and velocity are
perpendicular to B
Solenoid with increasing current I which induces an emf
in the (yellow) wire. An induced current I’ is moved
through the (yellow) wire by an induced electric field E
in the wire.
Eddy currents
formed by induced emf in a rotating metal disk.
Metal detector – an alternating magnetic field Bo
induces eddy currents in a conducting object moved
through the detector. The eddy currents in turn
produce an alternating magnetic field B’ and this field
induces a current in the detector’s receiver coil.
DISPLACEMENT
CURRENT
A capacitor being charged by a current iC has a
“displacement current” between the plates equal to iC ,
with displacement current iD = e A dE/dt. This
changing E field can be regarded as the source of the
magnetic field between the plates. ( E _ B )
A capacitor being charged by a current iC has a
displacement current equal to iC between the plates,
with
displacement current iD = e A dE/dt
From C = e A / d and DV = E d we can use
q = C V to get
q = (e A / d ) (E d ) = e E A = e F E and
from iC = dq / dt = e A dE / dt = e dF E / dt = iD
We now see that a
changing E field can produce a B field,
and from Faraday’s Law, a
changing B field can produce an E field or emf.
C 2011 J. Becker
MAXWELL’S EQUATIONS
The relationships between
electric and magnetic fields
and their sources can be
stated compactly in four
equations, called
Maxwell’s equations.
Together they form a
complete basis for the
relation of E and B fields to
their sources.
C 2004 Pearson Educational / Addison Wesley
Determine
direction of
induced
current for
a) increasing B
b) decreasing B
Lenz’s law
(Exercise 29.16)
Lenz’s law (Exercise 29.17)
Lenz’s law (Exercise 29.18)
Motional emf and Lenz’s law
(Exercise 29.21)
Motional emf and Lenz’s law
(Exercise 29.26)
TRANSFORMERS
can step-up AC voltages
or step-down AC voltages.
Lenz’s law (Exercise 29.18)
e = -N dF B / dt
TRANSFORMERS
can step-up AC
voltages or stepdown AC voltages.
e2 /e1 = N /N
2
V1I1 = V2I1
1
FB = FB
Transformer: AC source is V1 and secondary provides a
voltage V2 to a device with resistance R.
Figure 32.2b
Large step-down transformers at power stations are
immersed in tanks of oil for insulation and cooling.
Figure 31.22
Figure 31.23
Review
See
www.physics.sjsu.edu/becker/physics51
C 2012 J. F. Becker