Download lecture 29 motional emf

LECTURE 29
MOTIONAL EMF
Instructor: Kazumi Tolich
Lecture 29
2
! 
Reading chapter 23-4 to 23-5.
!  Motional
emf
!  Mechanical work and electrical energy
Motional emf
3
This conducting rod
completes the circuit.
!  As it falls, the magnetic
flux decreases, and a
current is induced.
!  The motion of the rod
produces a motional
emf in the system.
! 
Direction of the induced current
4
To oppose the decrease in magnetic flux through the
loop, the induced current must flow in a direction
that strengthens the magnetic field within the loop.
!  The force due to the induced current is upward,
slowing the fall.
! 
Eddy currents
5
! 
! 
! 
Currents can also flow in bulk conductors.
Consider a sheet of conductor pulled through a magnetic
field. There will be induced current called eddy currents
although there are now no well-defined current paths.
The magnetic force due to the eddy currents opposes the
motion of the conductor to the right.
Eddy currents: 2
6
! 
Eddy currents can be reduced by increasing the
resistance of the possible paths for the eddy
currents.
Insulating glue between the
metal slabs.
Slots cut into the metal slab.
Clicker question: 1
7
Demo: 1
8
Magnet down a copper tube
!  Magnet down an aluminum channel
! 
!  Demonstration
of eddy current and magnetic force
Demo: 2
9
! 
Magnetic damping pendulum
!  Demonstration
of eddy current and magnetic force
Triple beam balance damping
10
A metal plate attached to the balance arm passes
between the poles of a permanent magnet.
!  The induced eddy current provides the damping.
! 
Demo: 3
11
! 
Flying ring
!  Demonstration
of eddy current and magnetic force
Induction stove
12
! 
! 
! 
! 
A conducting coil just beneath the cooking surface carries an
oscillating current, producing an oscillating magnetic field.
This induces an oscillating eddy current in the conducting
cooking pan.
Due to the resistance of the pan, this eddy current heats up
the pan.
The cooking surface itself might never get hot.
Metal detectors and traffic lights
13
! 
! 
Metal detectors operate by
induced currents.
High frequency alternating
current flows in the transmitter
coil, which induces eddy current in
conductors nearby. The induced B
due to the eddy current opposes
the change in the field from the
transmitter. A receiver coil detects
the reduction in the magnetic
fields from the transmitter and
registers the presence of metal.
Motional emf: quantitative
14
! 
! 
An upward magnetic force qvB is on the
positive charge carrier moving horizontally
with the rod.
The charge carriers continue to move upward
until the electric force due to the E field by the
separated charge is balanced by the
magnetic force.
FE = FB
qE = qvB
E = vB
E = El = vBl
Example: 1
15
! 
A Boeing KC-135A airplane has
a wingspan of L = 39.9 m and
flies at constant altitude in a
northerly direction with a speed
of v = 240 m/s. If the vertical
component of the Earth’s
magnetic field is
Bv = 5.0 × 10-6 T, and its
horizontal component is
Bh = 1.4 × 10-6 T, what is the
induced emf between the wing
tips?
Motional emf: quantitative 2
16
! 
As the rod moves to the right at a constant velocity v,
the motional emf is given by
E =N
! 
ΔΦ BΔA
lvΔt
=
=B
= Bvl
Δt
Δt
Δt
The electric field caused by the motion of the rod is
E = El = Bvl
E = Bv
! 
The induced current is
E
Bvl
I=
=
R
R
Forces on the rod
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If the rod is to move at a constant speed, an
external force must be exerted on it.
!  This force should have equal magnitude and
opposite direction to the magnetic force:
! 
Mechanical and electric powers
18
! 
The mechanical power delivered by the external force is:
! 
Compare this to the electrical power in the light bulb:
! 
Therefore, mechanical power has been converted directly into
electrical power.
Clicker question: 2 & 3
19
Example: 2
20
! 
In the figure, let the magnetic field strength be
B = 0.80 T, the rod speed be v = 10 m/s, the
rod length be l = 0.20 m, and the resistance of
the resistor be R = 2.0 Ω. (The resistance of the
rod and rails are negligible.)
a) 
Find the induced emf in the circuit
b) 
Find the induced current in the circuit
(including direction).
c) 
Find the force needed to move the rod with
constant speed (assuming negligible friction).
d) 
Find the power delivered by the force found
in Part c).
e) 
Find the rate of Joule heating in the resistor.