# 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
Faraday’s Law of Induction
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,
and from Faraday’s Law, a
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
```