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)  = 90 o

DC generator  = 90 o

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 ( e ): e = v B L because the potential difference between a and b is e = D V = energy / charge = W/q e = 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 c has a displacement current equal to i C between the plates, with displacement current i D = 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 i C has a displacement current equal to i C between the plates, with 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. 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 Review C 2009 J. Becker