Electromagnetic Induction Ch. 29

Induction experiments Faraday’s law Lenz’s law Motional electromotive force (sec. 29.4) Induced electric fields (sec. 29.3) (sec. 29.5) Displacement Current (sec. 29.1) (sec. 29.2) (sec. 29.7)

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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 = 90

o

Alternator (AC generator)

f = 90

o

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

= v B L

e because the potential difference between a and b is

=

D e V = energy / charge = W/q

=

D V = work / charge D V = F x distance / q D V = (q v B) L / q so e

= v B L 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 i displacement current equal to i with displacement current i

D

= e

C

field between the plates.

c

has a between the plates, A dE/dt. This changing E field can be regarded as the source of the magnetic

A capacitor being charged by a current i

C

displacement current equal to i

C

with has a between the plates,

displacement current i

D

=

e

A dE/dt

From C = e A / d and D V = E d we can use

q = C V to get q = (

e

A / d ) (E d ) =

e

E A =

e F E and from i

C

= dq / dt = e

A dE / dt =

e

d

F E

/ dt = i

D

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.

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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.

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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