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

Electromagnetic Induction Ch. 29

C 2009 J. Becker

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

Lenz’s Law: The induced emf or current always tends to oppose or cancel the change that caused it.

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.

Alternator (AC generator)

= 90o

DC generator

= 90o

Slidewire generator

Magnetic force (F = IL x B) due to the induced current is toward the left, opposite to v.

Lenz’s law

Lenz’s Law: The induced emf or current always tends to oppose or cancel the change that caused it.

Currents (I) induced in a wire loop.

Motional induced emf ():

= v B L

because the potential difference between a and b is

= V = energy / charge = W/q

= V = work / charge V = F x distance / q

V = (q v B) L / qso

= 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 ic has a displacement current equal to iC between the

plates, with displacement current iD = 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 = A dE/dt

From C = A / d and V = E d we can use q = C V to get

q = ( A / d ) (E d ) = E A = and

from iC = dq / dt = A dE / dt = d/ 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

C 2004 Pearson Educational / Addison Wesley

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.

Lenz’s law (Exercise 29.16)

Determine direction of induced current for a) increasing B b) decreasing B

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)

See www.physics.edu/becker/physics51

Review

C 2009 J. Becker