PHYS 219 General Physics: Electricity, Light
and Modern Physics
Exam 1 is scheduled on Wednesday, February 13 @ 8 – 10 PM
It will cover four Chapters 17, 18, 19, and 20.
Physics Room 203 for those whose last names start with A - N
Physics Room 331 for those whose last names start with P - Z
Reviewing lecture notes, home works, and recitation problems !
EXAMS:
There will be two 75-minute evening exams and a two-hour final exam. The evening exams
are multiple-choice and should be able to be completed within 75 minutes by a well-prepared
student; note that we’re giving you 120 minutes. The times and locations of the evening
exams are as follows:
Exam 1: Wednesday, February 13 @ 8 – 10 PM in Physics 203 and Physics 331
Exam 2: Tuesday, March 26
@ 8 – 10 PM
in Physics 114
All exams are closed book. For the exams you will need a #2 pencil, a calculator and your
student ID. You may make a single crib sheet for Exam 1 (you may write on both sides of an
8.5” x 11” sheet of paper). Bring this and a second crib sheet to Exam 2; bring both crib
sheets and a third to the Final Exam. Many, but not all, formulae will be provided on the front
of the Exams.
Review of Chapters 17, 18, 19, and 20 – Lecture 11
Physics 219 Equation Sheet for Exam I (to be handed out) - 1
Physics 219 Equation Sheet for Exam I (to be handed out) - 2
Physics 219 Equation Sheet for Exam I (to be handed out) - 3
Chapter 20 Magnetic Fields and Forces – Lecture 10
20.1 Sources of Magnetic Fields
20.2 Magnetic Forces Involving Bar magnets
20.3 Magnetic Forces on a Moving Charge
20.4 Magnetic Forces on an Electric Current
20.5 Torque on a Current Loop and Magnetic Moments
20.6 Motion of Charged Particles in the Presence of
Electric and Magnetic Fields
20.7 Calculating the Magnetic Field: Ampere’s Law
20.8 Magnetic Materials: What Goes On Inside ?
20.9 The Earth’s Magnetic Field
20.10 Applications of Magnetism
Problem Solving Strategy
Problem 20.55
A long current-carrying wire lies on the y-axis and carries
Current I = 4.5 A along the + y direction. A magnetic field of
magnitude B = 1.2 T lies in the y-z plane directed 30o ,
away from the y- axis, as shown in Figure P20.55.
(a) What is the direction of the magnetic force on the wire ?
(b) What is the magnitude of the magnetic force
on a 1.0-m-long section of the wire ?
Figure P20.55 (p707)
Problem Solving Strategy, cont.
(1) Recognize the principle. The direction of the force
on the wire can be found using right-hand rule #1. The
magnitude of the force is related to the current, the field
magnitude, the length of the wire segment, and the
angle between the directions of the current flow and the
magnetic field.
(2) Sketch the problem.
See Figure P20.55.
(3) Identify the relationships. There is no simple
mathematical relationship to find the direction of the
force. The magnitude of the magnetic force on a currentcarrying wire is given by:
Fon wire = ILB sin θ
Problem Solving Strategy, cont.
(5) Solve. (a) Pointing your fingers in the direction of the
current flow (+y direction) and rotating them into the direction
of the field (30° above the +y direction), your thumb points in
the +x direction. Therefore, the force is in the +x direction
(b) Substituting into the equation
Fon wire = (4.5 A)(1.0 m)(1.2 T)sin30o = 2.7 N
(6) What does it mean? The force is perpendicular to the
plane containing the direction of current flow and the direction
of the magnetic field.
The magnitude of the force would be larger if the field and
direction of current flow were perpendicular to each other (θ =
900).
Ampère’s Law
• There are two ways to calculate the magnetic field
produced by a current
• One way treats each small piece of wire as a separate
source
•
•
Similar to using Coulomb’s Law for an electric field
Mathematically complicated
• Second way is to use Ampère’s Law
•
•
Most useful when the field lines have high symmetry
Similar to using Gauss’s Law for an electric field
Section 20.7
Ampère’s Law, cont.
• Relates the magnetic
field along a path to the
electric current
enclosed by the path
• For the path shown,
Ampère’s Law states
that
 B L  o Ienclosed
closed
path
 B  dl   I
0 enclosed
• μo is the permeability
of free space
• μo = 4 π x 10-7 T . m / A
Section 20.7
Magnetic Field of a Long Straight Wire
• If B varies along the path, Ampère’s Law can be
•
•
•
•
very difficult to apply in practice
Ampère’s Law can be used to find the magnetic field
near a long, straight wire
B|| is the same all along the path
If the circular path has a radius r, then the total path
length is 2 π r
Applying Ampère’s Law gives
o I
  B L  o Ienclosed
B
2 r
closed
path
for a straight wire current
 B  dl   I
0 enclosed
Section 20.7
Field from a Current Loop
• It is not possible to find a
path along which the
magnetic field is constant
• So Ampère’s Law cannot be
easily applied
• From other techniques, the
field at the center of the loop
o I
is
B
2R
for a circular loop of current
• Reminder: For a straight wire
o I
current (Ampère’s Law) B 
2 r
Section 20.7
Field Inside a Solenoid
• By stacking many loops close together, the field
along the axis is much larger than for a single loop
• A helical winding of wire is called a solenoid
• More practical than stacking single loops
Section 20.7
Solenoid, cont.
• For a very long
solenoid, it is a good
approximation to
assume the field is
constant inside the
solenoid and zero
outside
• Use the path shown in
the figure
• Only side 1 contributes
to the magnetic field
Section 20.7
Ampere’s Law applied to a ideal solenoid
• Long solenoid (a<<L):
B inside solenoid
// to axis
B outside solenoid
nearly zero
a
(not very close to the ends or wires)
• Ampere’s Law:
 B L  o Ienclosed
closed
path
Ienclosed =nhI
length)
N
n
L
 B  dl   I
 B  dl  Bh
0 enclosed
(n windings per unit
B  μ 0n I
for an ideal solenoid
L
Magnetic Fields of Solenoids (1)
(Magnetic field lines for solenoid with 600 turns)
16
Magnetic Fields of Solenoids (2)
• To create a uniform field, a solenoid is used consisting of many loops
wound close together
• Solenoids are commonly used in electric valves and other electro-
mechanical devices
Magnetic Materials
• Magnetic poles always come in pairs
• To understand why, the atomic origin of permanent
magnetism must be considered
Section 20.8
Magnetic Moment
• For a current loop, the
magnetic moment is I A
• The direction of the
magnetic moment is
either along the axis of
the bar magnet or
perpendicular to the
current loop
• The strength of the
torque depends on the
magnitude of the
magnetic moment
Section 20.5
Circular Loop Current as a Magnetic Dipole
B  Bx 
0 I
2R

R3
2
R
 x

2 3/2

0 I
2
R
0 2 
  IAnˆ  I  R nˆ  Bx 
4 x 3
2
2
1
x
3
if |x|>>R
Ex 
1 2p
4 0 x 3
On electric dipole axis
p = q r(+-)
Motion of Electrons
• The motion of an electron around a nucleus can be
pictured as a tiny current loop
• The radius is approximately the radius of the atom
• The direction of the resulting magnetic field is
determined by the orientation of the current loop
Section 20.8
Electron Spin
• The electron also
produces a magnetic
field due to an effect
called electron spin
• The spinning charge
acts as a circulating
electric current
• The electron has a spin
magnetic moment
Section 20.8
Electron Spin, cont.
• When an electron is
placed in a magnetic
field, it will tend to align
its spin magnetic
moment with the
magnetic field
Section 20.8
Magnetic Field in an Atom
• The correct explanation of electron spin requires
quantum mechanics
• Confirms an atom can produce a magnetic field in
two ways
• Through the electron’s orbital current loop
• Through the electron’s spin
• The total magnetic field produced by a single atom is
the sum of these two fields
Section 20.8
Magnetic Field from Atoms, cont.
• Each atom produces a
current loop
• The collection of small
current loops acts as one
large loop
• This produces the
magnetic field in the
magnetic material
• The current in each
atomic loop is very small,
but the large number of
atoms results in a large
effective current
Section 20.8
Atomic Magnets to Permanent Magnets
• Not all atoms will actually be magnetic since the
current loops of different electrons can point in
different directions
• Their magnetic fields could cancel
• The total magnetic field will depend on how the
atomic magnetic fields are aligned
• A permanent magnet has the atomic fields aligned
Section 20.8
Isolated Magnetic Poles
• A bar magnet is
produced by a collection
of aligned atomic-scale
current loops
• Cutting the magnet in
half produces two new
complete bar magnets
• Each resulting piece still
produces the magnetic
field of a complete bar
magnet with a north and
south pole
Section 20.8
Magnetic Domains
• It is possible for the atomic
magnets in different
regions within a magnetic
material to point in different
directions
• Called magnetic domains
• The arrangement shown is
equivalent to two bar
magnets
• Because the atomic
magnets are aligned in
opposite directions, this
would appear to be
nonmagnetic
Section 20.8
Properties of Magnetic Domains
• A material has two
domains of
approximately the same
size
• Apply a magnetic field
from a bar magnet
• The domain aligned
with the magnetic field
grows at the expense of
the other domain
• The material now acts
like a bar magnet
Section 20.8
Earth’s Magnetic Field
• The Earth acts like a
very large magnet
• A compass needle
aligns with its north
magnetic pole pointing
approximately toward
the Earth’s geographic
north pole
• So the Earth’s
geographic north pole
is actually a south
magnetic pole
Section 20.9
Earth’s Magnetic Field, cont.
• The location of the Earth’s south magnetic pole
does not correspond exactly with the geographic
north pole ( ~11o currently)
• The Earth’s south magnetic pole moves slowly
• Currently at about 40 km/year
• The Earth’s magnetic field has completely reversed
direction (~170 times in the past 100 million years –
The last reversal occurred about 770,000 years ago)
• The field is probably produced by electric currents in
the core by spinning liquid metals
Section 20.9
Cosmic Rays
• Charged particles from
•
•
•
•
space are called cosmic
rays
Their motion is affected by
the Earth’s magnetic field
At the equator, the particles
are deflected away from
the Earth’s surface
At the poles, the particles
follow a helical path and
spiral into the poles
They interact with the
Earth’s atmosphere and
produce aurora
Section 20.9
Applications of Magnetism
• Magnetism is used by doctors, engineers,
archeologists, and others
• Applications include
• Blood-flow meters
• Relays
• Electric motors (Demo)
• Bacteria
• Magnetic dating
Section 20.10
Electric Motor
• A magnetic field can produce a torque on a current loop
• If the loop is attached to a rotating shaft, an electric motor
is formed
• In a practical motor, a solenoid is used instead of a single
loop
• Reversal of the current (using a commutator) is needed to
keep the shaft rotating
Section 20.10
Demo – Electric Motor
S
N
N
S
S
N
Current direction is switched using a commutator
Commutator Ring in Motors and Generators