Induction experiments(sec. 29.1) Faraday’s law (sec. 29.2) Lenz’s law(sec. 29.3) Motional...

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