Announcements
• WebAssign HW Set 7 due this Friday
• Problems cover material from Chapters 20
• Estimated course grades available on e-learning
• Office hours:
• Tea and Cookies with Prof. Kumar, 5 pm today, room 2165
• My office hours Th 2-3 pm
• or make an appointment
• Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/
for more announcements
QUESTIONS? PLEASE ASK!
From last time…


Ampere’s Law
B|| Δℓ = µo I
Magnetic Field for a long straight
mo I
wire:
B =

Magnetic Force between long straight
wires:
mo I 1 I 2
F
=

2p r
2p d
Magnetic Field of a current loop:
B =N

mo I
2R
Magnetic Field of a solenoid:
B = µo n I
http://www.scienceprog.com/the-great-pll-induction-heater-driver/
Chapter 20
Induced Voltages and
Inductance
http://science.howstuffworks.com/rail-gun1.htm
http://www.ecvv.com/product/1474115.html
Faraday’s Experiment

A current can be produced by a
changing magnetic field…




Faraday’s insight: An electrical
current is produced by a changing
magnetic field


When the switch is closed, the ammeter
reads a current and then returns to zero
When the switch is opened, the
ammeter reads a current in the opposite
direction and then returns to zero
When there is a steady current in the
primary circuit, the ammeter reads zero
The secondary circuit acts as if a source
of emf were connected to it for a short
time
Conclusion: an induced emf is
produced in the secondary circuit
by the changing magnetic field
Magnetic Flux

emf is induced by a change in the magnetic
flux, ΦB, not simply by a change in the
magnetic field


Magnetic flux is defined in a manner similar to
that of electrical flux
The flux is defined as ΦB = BA = B A cos θ





θ is the angle between B and the normal to
the plane
The wire is in a magnetic field
The loop has an area A
SI units of flux are T. m² = Wb (Weber)
The value of the magnetic flux is
proportional to the total number of
lines passing through the loop
Example Problem 20.16

A circular coil enclosing an area of 100 cm2 is
made up of 200 turns of copper wire. The wire
making up the coil has a resistance of 5 Ω, and
the ends of the wire are connected to form a
closed circuit. Initially, a 1.1 T uniform magnetic
field points perpendicularly up through the plane
of the coil. The direction is then reversed so that
the final magnetic field has a magnitude of 1.1 T
and points down through the coil. If the time
required to reverse directions is 0.10 s, what
average current flows through the coil during
that time?
Electromagnetic Induction and
Faraday’s Law

A current is set up in the circuit as long as there is
relative motion between the magnet and solenoid




The same experimental results are found whether the loop
moves or the magnet moves
The current is an induced current because is it produced
by an induced emf
Faraday’s Law: The instantaneous emf induced in a
circuit equals the time rate of change of magnetic flux
through the circuit
If a circuit contains N tightly wound loops and the flux
changes by ΔΦB during a time interval Δt, the average
emf induced is given by Faraday’s Law:
e = -N
DF B
Dt
Faraday’s Law and Lenz’
Law

ΔΦB, can be produced by a change in
B, A or θ


The negative sign in Faraday’s Law is
very important, and come about by
Lenz’ Law



Since ΦB = B A cos θ
The current caused by the induced emf
travels in the direction that creates a
magnetic field with flux opposing the
change in the original flux through the
circuit
Example: suppose in the figure, B
becomes smaller with time

This reduces the flux
The induced current will produce an
induced field, Bind , in the same
direction as the original field
e = -N
DF B
Dt
20.3 Motional EMF


Suppose a straight conductor of
length ℓ moves perpendicularly
with constant velocity through a
uniform field
The electrons in the conductor
experience a magnetic force


Recall FM = q v B
The electrons move down and pile
up at the bottom of the conductor,
leaving a net positive charge at
the top of the conductor
Motional EMF

As a result of this charge
separation, an E field (and FE
= qE is produced)…

Electrons continue to move
down until FM = FE
qvB=qEE=vB

…leading to a potential
difference, DV, across the
conductor
ΔV = E l = B ℓ v

The top is at a higher potential
Motional EMF in a Circuit

Now place the conductor on
a pair of rails and pull it
with an applied force Fapp


assume the moving bar
has negligible resistance
The magnetic force Fapp on
the charges sets up an
induced current

the charges are free to
move in the closed path!
Motional emf in a Circuit,
cont


The changing magnetic
flux through the loop
and the corresponding
induced emf in the bar
result from the change
in area of the loop
The induced ‘motional’
EMF acts like a battery
in the circuit
B v
e = B v and I =
R
Example Problem 20.21

An automobile has a vertical radio antenna 1.20
m long. The automobile travels at a 65.0 km/h
on a horizontal road where the earth’s magnetic
field is 50.0 μT, directed toward the north and
downward at an angle of 65° below the
horizontal. (a) Specify the direction the
automobile hsould move so as to generate the
maximal motional emf in the antenna, with the
top of the antenna positive relative to the
bottom. (b) Calculate the magnitude of the
induced emf.
Solution to 20.16
Solution to 20.21