Physics 202, Lecture 15
Today’s Topics
!! Faraday’s Law (Ch 28)
!! Change of Magnetic Flux and Emf (!)
"! Electromotive “force”, emf, is a measure of the voltage
that can be provided by a source.
#! For a given device, if a charge Q passes through that
device, and gains an energy U, the net emf for that
device is the energy gained per unit charge, or U/Q.
#! emf is not a force, it has a unit of volts
#! sources of emf:
!= 1.5V
+
•! chemical process (battery)
+++++
•! change of magnetic flux
+
•! semiconductors…..
"!e.g. battery:
#! notice that emf has a direction
------#! emf may exist even if no current.
1.5V
!! Lenz’s Law
!! Faraday’s Law of Induction
Electromotive Force (emf, !)
Demo: Emf and Change of Magnetic Flux
Lenz’s Law
"!The emf due to change of magnetic flux tends to
create a current which produces a magnetic field to
compensate the change of original magnetic flux.
#! Lenz’s law is a convenient way to determine the
direction of the emf due to magnetic flux change.
Demo: Eddy Current
Quizzes/Exercises: Determine Direction Of emf
"! Indicate the direction of emf in the following cases:
............
+++++++++
+++++++++
............
+++++++++
+++++++++
+++++++++
+++++++++
............
B ............
+++++++++
+++++++++
+++++++++
+++++++++
............
+++++++++
+++++++++
............
|B| increases
|B| decreases
|B| decreases
............
............
............
B ............
............
............
|B| increases
+++++++
+++++++
+++++++
+++++++
+++++++
path
outside B
or
|B| decreases
Formulation of Faraday’s Law
Direction of Induced emf
"!The emf induced in a “circuit” is proportional to the
time rate of change of magnetic flux through the
“circuit”.
#
nominal
#
d! B
="
dt
direction of
"! Notes:
#! “Circuit”: any closed path
$!does not have to be
real conducting circuit
#! The path/circuit does not
have to be circular, or even planar
!#
B
"#
d! B
="
dt
nominal
direction of
!#
B
"! !>0, same as nominal direction
!<0, opposite
A
" B = ! B • dA
"! Note that the nominal direction
of ! and the direction of vector A
follows right hand rule
"#
A
" B = ! B • dA
Methods to Change Electric Flux
" = # d$ B = # d ( BA cos! )
dt uniform B
dt
"!Change of $B! emf
%! To change $B:
#! Change B ! emf produced by an induced E field
#! Change A ! motional emf
#! Change ! ! motional emf
#! Combination of above
Points C and D are fixed. Point P moves as
y = A cos ωt, A = 5cm, f =
Conductor
P
ω
= 10Hz
2π
.
.
B
D
C
Calculate the EMF in between points C and D
Distance between C and D is L=1m and B=2T
L
L
ΦB = B y = B A cos ωt
2
2
dΦB
L d cos ωt
L
!=−
= −B A
= B Aω sin ωt
dt
2
dt
2
! = π sin ωt (V olts)