# Document ```Electromagnetic Induction Ch. 29
Induction experiments
Lenz’s law
Motional electromotive force
Induced electric fields
Displacement Current
C 2009 J. Becker
(sec. 29.1)
(sec. 29.2)
(sec. 29.3)
(sec. 29.4)
(sec. 29.5)
(sec. 29.7)
Current induced in a coil.
When B is constant and
shape, location, and
orientation of coil does
not change, the induced
current is zero.
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.
Lenz’s law
How electric generators, credit card readers, and
transformers work.
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 v.
Lenz’s Law:
The induced emf or
current always
tends to oppose or
cancel the change
that caused it.
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.
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. This changing
E field can be regarded as the source of the magnetic
field between the plates.
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 have now seen that a
changing E field can produce a B field,
changing B field can produce an E field or emf.
C 2009 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 29.22)
Motional emf and Lenz’s law
(Exercise 29.25)
Review
See www.physics.edu/becker/physics51
C 2009 J. Becker
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