Physics 1402: Lecture 13
Today’s Agenda
• Announcements:
– Lectures posted on:
www.phys.uconn.edu/~rcote/
– HW assignments, solutions etc.
• Homework #4:
– On Masterphysics : due Friday at 8:00 AM
– Go to masteringphysics.com
• Midterm 1: next week (Oct. 5)
– Covers Ch. 21-26
Problem Solution
Method:
Five Steps:
1) Focus on the Problem
-
draw a picture – what are we asking for?
2) Describe the physics
-
what physics ideas are applicable
what are the relevant variables known and unknown
3) Plan the solution
-
what are the relevant physics equations
4) Execute the plan
-
solve in terms of variables
solve in terms of numbers
5) Evaluate the answer
-
are the dimensions and units correct?
do the numbers make sense?
Magnetism
The Magnetic Force
B
x x x x x x
x x x x x x
v
x x x x x x
F q
B
B

v

 q
F
x x x x x x x x x x x x
x x x x x x x x x x x v
x B
x x x x x x x x x x x x
v
F
F q
v
q
F=0
Magnetism
•
Magnetic effects from natural magnets have been known for a
long time. Recorded observations from the Greeks more than
2500 years ago.
•
The word magnetism comes from the Greek word for a certain
type of stone (lodestone) containing iron oxide found in
Magnesia, a district in northern Greece – or maybe it comes
from a shepherd named Magnes who got the stuff stuck to the
nails in his shoes
•
Properties of lodestones: could exert forces on similar stones
and could impart this property (magnetize) to a piece of iron it
touched.
•
Small sliver of lodestone suspended with a string will always
align itself in a north-south direction. ie can detect the
magnetic field produced by the earth itself. This is a compass.
Bar Magnet
• Bar magnet ... two poles: N and S
Like poles repel; Unlike poles attract.
• Magnetic Field lines: (defined in same way as electric
field lines, direction and density)
S
N
You can see this
field by bringing
a magnet near a
sheet covered
with iron filings
• Does this remind you of a similar case in electrostatics?
Electric Field Lines
of an Electric Dipole
Magnetic Field Lines of
a bar magnet
S
N
Magnetic Monopoles
• One explanation: there exists magnetic charge, just like
electric charge. An entity which carried this magnetic
charge would be called a magnetic monopole (having + or magnetic charge).
• How can you isolate this magnetic charge?
Try cutting a bar magnet in half:
S
N
S
N
S
N
• In fact no attempt yet has been successful in finding
magnetic monopoles in nature.
• Many searches have been made
• The existence of a magnetic monopole could give an
explanation (within framework of QM) for the quantization of
electric charge (argument of P.A.M.Dirac)
Source of Magnetic Fields?
• What is the source of magnetic fields, if not magnetic
charge?
• Answer: electric charge in motion!
– eg current in wire surrounding cylinder (solenoid)
produces very similar field to that of bar magnet.
• Therefore, understanding source of field generated by bar
magnet lies in understanding currents at atomic level
within bulk matter.
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
Forces due to Magnetic Fields?
•
Electrically charged particles come under various sorts of forces.
•
As we have already seen, an electric field provides a force to a
charged particle, F = qE.
•
Magnets exert forces on other magnets.
•
Also, a magnetic field provides a force to a charged particle, but
this force is in a direction perpendicular to the direction of the
magnetic field.
Definition of Magnetic Field
Magnetic field B is defined operationally by the magnetic
force on a test charge.
(We did this to talk about the electric field too)
• What is "magnetic force"? How is it distinguished from
"electric" force?
Start with some observations: CRT deflection
• Empirical facts: a) magnitude:  to velocity of q
b) direction: ^ to direction of q
q
v
F mag
Lorentz Force
• The force F on a charge q moving with velocity v
through a region of space with electric field E and
magnetic field B is given by:
B
x x x x x x
B

x x x x x x
v
x x x x x x
q
F
v

 q
F
Units:
1 T (tesla) = 1 N / Am
1G (gauss) = 10-4 T
B
v
q
F=0
1
Lecture 13, ACT 1
•
2A
Two protons each move at speed v (as shown in the
diagram) toward a region of space which contains a
constant B field in the -y-direction.
– What is the relation between the magnitudes of the
forces on the two protons?
y
1
B
2
z
(a) F1 < F2
(b) F1 = F2
v
(c) F1 > F2
v
x
Lecture 13, ACT 1
•
2A
Two protons each move at speed v (as shown in the
diagram) toward a region of space which contains a
constant B field in the -y-direction.
– What is the relation between the magnitudes of the
forces on the two protons?
y
1
B
2
z
(a) F1 < F2
(b) F1 = F2
v
(c) F1 > F2
v
x
Lecture 13, ACT 1
y X F1
• Two protons each move at speed v (as
v
shown in the diagram) toward a region of
1
space which contains a constant B field in
F2 X
the -y-direction.
v
2
z
1B
B
x
– What is F2x, the x-component of the force on the second
proton?
(a) F2x < 0
(b) F2x = 0
(c) F2x > 0
Lecture 13, ACT 2
• Cosmic rays (atomic nuclei stripped bare of their
electrons) would continuously bombard Earth’s
surface if most of them were not deflected by
Earth’s magnetic field. Given that Earth is, to an
excellent approximation, a magnetic dipole, the
intensity of cosmic rays bombarding its surface is
greatest at the (The rays approach the earth
radially from all directions).
A) Poles
B) Equator
C) Mid-lattitudes
Magnetic Force
on a Current
• Consider a current-carrying wire in the
presence of a magnetic field B.
N
• There will be a force on each of the charges
moving in the wire. What will be the total force
dF on a length dl of the wire?
• Suppose current is made up of n
charges/volume each carrying charge q and
moving with velocity v through a wire of crosssection A.
• Force on each charge =
• Total force =
• Current =
Simpler: For a straight length of wire L carrying
a current I, the force on it is:

S