Download Example 20-1.

Upcoming Schedule
Oct. 20
review
Oct. 27
20.3-20.6
Nov. 3
21.1-21.2
Oct. 22
Exam 2
Ch. 18, 19
Oct. 24
20.1-20.2
Oct. 29
boardwork
Oct. 31
20.7-20.8
Quiz 6?
Nov. 5
boardwork
Nov. 7
21.3-21.5
Quiz 7?
“A mathematician may say anything he pleases, but a physicist must be at
least partially sane.”—J. Willard Gibbs
Assignment for Monday, October 27:
Read 20.1-20.3
Work 20.3, 20.5, 20.7
I will lecture on 20.3-20.6
I’ll post the assignments through exam 3 later today.
Chapter 20
Magnetism
20.1 Magnets and Magnetic Fields
We will study ferromagnetism in this lecture.
It is so named because many ferromagnetic
materials (including the first-discovered ones) are
“ferrous materials,” i.e., they contain iron.
We have studied electric forces and electric fields.
Now we study magnetism and magnetic fields.
Rather than defining magnetism, we begin by discussing
properties of magnetic materials.
Recall how there are two kinds of charge (+ and -), and likes
repel, opposites attract.
Similarly, there are two kinds of magnetic poles (North and
South), and like poles repel, opposites attract.*
S
S
N
S
N
Repel
S
N
N
S
N
Repel
S
Attract
N
Thanks to Dr.
Waddill for
the nice
pictures!
S
N
N
S
Attract
*Recall also that I have a mental defect which often causes me to
say “likes attract and unlikes repel” when I mean the opposite. I
am not to be penalized for a mental defect!
There is one difference between magnetism and electricity: it is
possible to have isolated + or – electric charges, but isolated N
and S poles have never been observed.
-
+
N
S
I.E., every magnet has BOTH a N and a S pole, no how many
times you “chop it up.”
S
N
=
S
N
+ S
N
The earth has associated with it a magnetic field, with poles
near the geographic poles.
The pole of a magnet attracted to
the earth’s north geographic pole is
the magnet’s North pole.
N
The pole of a magnet attracted to
the earth’s south geographic pole
is the magnet’s South pole.
S
http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/ma
gearth.html
Just as we used the electric field to help us “explain” and
visualize electric forces in space, we use the magnetic field to
help us “explain” and visualize magnetic forces in space.
Magnetic field lines point in the same direction that the north
pole of a compass would point.
Magnetic field lines are tangent to the magnetic field.
The more magnetic field lines in a region in space, the stronger
the magnetic field.
Outside the magnet, magnetic field lines point away from N
poles (*why?).
Huh?
Nooooooo….
Yesssssss….
*The N pole of a compass would “want to get to” the S pole of the magnet.
Is the earth’s north pole a magnetic N or a magnetic S?
It has to be a S, otherwise, the
compass N would not point to it.
Unless the N of a compass needle is
really S. Dang! This is too much
for me!
Yup, it’s confusing.
Here’s a “picture” of the magnetic
field of a bar magnet, using iron
filings to map out the field.
The magnetic field ought to “remind”
you of the earth’s field.
Later I’ll give a better definition for magnetic field
direction.
Here’s what the magnetic field looks like when you put unlike or
like poles next to each other.
The magnetic field B is a vector which points in the direction of
magnetic field lines. We will quantify the magnitude of B later.
Understand the declination, or angle of dip, if you plan to get
lost in the woods and use a compass to find your way out.
fs2002 lecture 11 ended here
Demonstration: electric current and magnetism.
20.2 Electric Current Produces Magnetism
An electric current produces a magnetic field.
The direction of the current is given by
the right-hand rule. Grasp the currentcarrying wire in your right hand, with
your thumb pointing in the direction of
the current. Curl your fingers around the
wire. Your fingers indicate the direction
of the magnetic field.
Picture on previous page is from
http://physics.mtsu.edu/~phys232/Lectures/
L12-L16/L17/Current_Loops/current_loops.html
This picture also illustrates the magnetic field due to a currentcarrying loop of wire.
These symbols mean “out
of page” and “into page.”
See next section.
Field comes out of
page here.
“Turns around” and
goes into page here.
Here’s a simpler case: the magnetic field due to a straight wire.
Field comes out
of page here.
Field turns
around and goes
into page here.
Thanks again to
Dr. Waddill for
the nice
pictures!
If the wire is grasped in the right hand with the thumb pointing
in the direction of the current, the fingers will curl in the
direction of B.
20.3 Force on an Electric Current in a Magnetic Field;
Definition of B
As seen above, an electric current gives rise to a magnetic field,
which must exert a force on a magnet (e.g. compass needle).
Does a magnet exert a force on a current-carrying wire?
(Newton’s 3rd Law says it should.)
Yes—a current-carrying wire in a magnetic field “feels” a force.
The direction is given by the right-hand rule:
Point your outstretched fingers in the direction of the current.
Bend your fingers 90º and orient your hand to point the bent
fingers in the direction of the magnetic field. Your thumb points
in the direction of the force.
Let’s practice! Isn’t it fun to make stupid physics gestures!
You may need to re-orient your hand as you go through this
procedure. During exams, I see all sorts of gyrations as
students try to figure out directions.
I’ll demonstrate another right-hand rule in class.
Here is a web “physics toy” to help you visualize the force on a
current-carrying conductor.
Below is another picture to help you visualize. It came from
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/forwir2.html.
The web page even has
a built-in calculator that
gives you numerical
answers to your force
problems!
The force is perpendicular to both the current and the magnetic
field.
You would expect the magnitude of the force to depend on the
magnitudes of the magnetic field and the current. In fact, it
does.
The force also depends on how much of the wire is in the
magnetic field.
If the direction of the current is perpendicular to the magnetic
field, then F = I ℓ B. I’ll write the lowercase l in italics (ℓ) to
help you distinguish it from the number 1.
If the current and magnetic field are not perpendicular, the
force magnitude is given by
F = I ℓ B sin ,
OSE:
where  is the angle between the current vector and the
magnetic field vector. (Smallest angle from the current vector
to the magnetic field vector.)
I
ℓ

B
No, that’s not a pencil. Can’t you tell it’s a wire?
The right-hand rule and the equation above actually serve as
the definition of the magnetic field B.
The SI unit for magnetic field is the tesla:
1 T = 1 N / (1 A · 1 m).
An older unit for magnetic field (which you might see
occasionally) is related to the weber (weber is 1 Wb = 1 N / 1
A). 1 T = 1 Wb / m2.
Magnetic fields are also given in units of gauss: 1 G = 10-4 T.
Argh! Confusing. Let’s try to stick with SI units, OK?
Here is a little movie I found on a web site (forgot where)
illustrating force on a wire due to magnetic field.
I have to go to a lot of effort to explain magnetic field and force
direction when I teach the non-calculus course.
It’s so much easier with calculus and vectors. The force on a
charge q moving with a velocity v in a magnetic field B is found
to obey F = qv  B.
The magnitude of the cross product is qvB sin . But it’s so
much easier learning the right-hand rule for the vector cross
product, and applying it to torques, charged particles, etc.,
instead of learning a seemingly new right hand rule for each
new topic. The elegance of math!
If you take a number of charged particles in a volume of wire
that has a length ℓ in a magnetic field, it is easy to derive the
vector form of our OSE: F = I  B.
The earth’s magnetic field has a
magnitude of roughly 0.5 G, or
0.0005 T. A powerful permanent
magnet, like the kind you might
find in headphones, might
produce a magnetic field of 1000
G, or 0.1 T.
http://liftoff.msfc.nasa.gov/academy/space/mag_field.html
The electromagnet in the basement
of Physics that my students use in
experiments can produce a field of
26000 G = 26 kG = 2.6 T.
Superconducting magnets can produce a field of
over 10 T. Never get near an operating superconducting magnet while wearing a watch or belt
buckle with iron in it!
Example 20-1. In the figure two slides back, B=0.9 T, I=30 A,
ℓ=12 cm, and =60°. What is the force on the wire?
F = I ℓ B sin  = (30 A) (0.12 m) (0.9 T) (sin 60°)
F = 2.8 N
Here’s a repeat of the figure, for handy reference.
I
ℓ

B
Hold it! Force is a vector quantity! What is the direction.
The force is perpendicular to both current direction and
magnetic field direction, so it is either into paper or out of the
paper. Apply either right-hand rule and you find it is into the
paper.
I’ll also show you (next slide) the right-hand screw rule, which
is the way I best visualize the direction.
We need to have a way to draw 3-d vectors on 2-d paper. We
will use the symbol
for a vector pointing directly out of the
page, towards us (that is supposed to look like the sharp point
of an arrowhead coming right towards your eye).
We will use the symbol  for a vector pointing directly into the
page, away from us (that is supposed to look like the feathered
end of an arrow going away from your eye).
I
ℓ

B
Here’s the right-hand screw rule. Imagine a “normal” (righthand) screw (you’re looking directly at the slotted end).
Use a mental screwdriver to turn the screw from the direction
of I towards B.
In this case, you would drive the screw into the plane of the
screen. Same direction as force.