Physics 202, Lecture 16Today’s Topics

Reminder of Lenz’s and Faraday’s Laws A Snapshot of the Maxwell Equations Eddy Currents

Forces due to Changing B are Nonconservative

Electric Generators

Lenz’s Law (Reminder) The emf due to change of magnetic flux tends to

created a current which produces a magnetic field tocompensate the change of original magnetic flux. Note: Real current may or may not generated. Lenz’s law is a convenient way to determine the

direction of the emf due to magnetic flux change.

Faraday’s Law (Reminder) The emf induced in a “circuit” is proportional to the

time rate of change of magnetic flux through the“circuit”.

Notes: “Circuit”: any closed path

does not have to be real conducting circuit

The path/circuit does not have to be circular, or even planar

dt

dB

!"=#

A

B

θ

! •=" AB dB

nominal direction of ε

Maxwell’s Equations

! =•0"

qdAE

!"

#=•dt

dd

BsE

BvEF !+= qq

!"

+=•dt

dId

E

000µ#µsB

! =• 0AB d

Gauss’s Law/ Coulomb’s Law

Faraday’s Law

Gauss’s Law of Magnetism, no magnetic charge

Ampere Maxwell Law

Also, Lorentz force Law

These are the foundations of the electromagnetism

Motional emf (Reminder) If a conducting segment are in relative motion (cut

through) with a magnetic field, an emf is produced. Motional emf is produced by the magnetic force

on the free particles inside the conductor Faraday’s law is also valid for this type of emf

Exercise: show that the motional emf inthe left fig. is ε=Blv+

-

Demo: Eddy Current

Demo: Jumping Ring and more

conducting ringv

switch on and the ring jumps

Induced E is not a Conservative Force

Whenever a magnetic field varies in time, an electricfield is induced.

+ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + +

!"

#=•dt

dd

BsE

Notes:• Induced E is not a conservative field.• Induced E can exist in a location where no B field exists. • Induced E is independent of circuit

valid for any closed pathA changing B field

Methods to Change Electric Flux

Change of ΦB emf To change ΦB:

Change B emf produced by an induced E field Change A motional emf Change θ motional emf Combination of above

dt

BAd

dt

d

uniform

)cos( !" #

$#= =

B

B

Electric Generators

Demo: Electric Generator

)sin()cos(

tNABdt

ABdN

dt

dN !!

"# =$=

%$= B

θ=ωt