Download 1 Exam 1: Exam 1: Magnetic Field Bar Magnets

Exam 1:
Exam 1:
*Covers all readings, lectures, homework from Chapters
17 through 19
*Exam 1: Tuesday September 28, 2010 from 8 PM - 10 PM
*The exam will be multiple choice and is meant to be done
within 75 minutes by a well-prepared student. We will
give 120 minutes starting promptly at the listed time, so
please be on time!
* Room PHYS 112 for last names A through K
* Room PHYS 114 for last names L through Z
Be sure to bring your student ID card,
calculator, pencil and your own one-page
(two-side) crib sheet.
NOTE THAT FEW EQUATIONS WILL BE GIVEN – YOU ARE REMINDED
THAT IT IS YOUR RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED
CRIB SHEET YOU WANT TO BRING TO THIS EXAM.
9/21/10
1
Magnetic Field
9/21/10
2
Bar Magnets
•  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
S
N
N
N
S
S
Attraction
•  Large Magnetic fields are used
in MRI (Nobel prize for
medicine in 2003)
•  Extremely Large magnetic field
are found in some stars
•  Earth has a Magnetic Field
9/21/10
N
S
3
9/21/10
N
Repulsion
From North to South
4
1
DEMO of Magnetic Field Lines
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).
Electric Field Lines
of an Electric Dipole
•  How can you isolate this magnetic charge?
Try cutting a bar magnet in half:
S
Magnetic Field Lines of
a bar magnet
S
9/21/10
N
S
N
S
N
•  In fact no attempt yet has been successful in finding
magnetic monopoles in nature but scientists are
looking for them.
N
5
Magnetic Force on a Moving Charge
9/21/10
6
Right Hand Rule
Direction of FB is perpendicular to plane containing v & B.
If q is positive, FB has the same sign as v x B.
If q is negative, FB has the opposite sign of v x B.

 
FB = qv × B

F = q vB sin φ
FB is never parallel to v.
FB can only change the direction of the particle not the speed.
9/21/10
7
9/21/10
8
2
More on Magnetic Force
The Magnetic Force

 
F = qv × B
•  The magnetic force on a charged object that moves in a
magnetic field does not do any work, because it’s
perpendicular to v.
•  The magnetic force cannot change the magnitude of the
velocity of a charged object, but can change the direction
of motion. B = steering wheel, E = accelerator or brake
pedal, so to speak
•  The SI unit for magnetic field is tesla (T):
1T =1
-4
~Earth’s surface
field!
B
B
x x x x x x
v
x x x x x x
+q
FB
N
N
N
=1
=1
C⋅m / s
C/s⋅m
A⋅m
A common unit gauss (G): 1 G = 10 T
9/21/10
B
x x x x x x
The direction of the force is:
v
v
x
+q
+q
FB (into the page)
FB=0 (sin(0)=0)
x x x x x x x x x x x x
x x x x x x x x x x x x
v B
x x x x x x x x x x x x
v
F
F q
9
9/21/10
10
Top view of Current-Carrying Bar Sliding on two
current carrying frictionless rails in a magnetic
field.
I
Magnetic Force on a Current-Carrying Wire
V
+
–
I
F
B
THIS IS A FORM
OF ELECTRIC
MOTOR, TURNING
ELECTRICAL INTO
MECHANICAL
ENERGY
Note that this example assumes that the magnetic field
caused by the currents in the rails is negligible compared to
the external magnetic field B shown.
I
motion by reversing
Direction of I, by reversing V
The length L is the distance between the rails, where B is and
where the current I flows in the green bar.
9/21/10
11
9/21/10
DEMO
12
3
Motion of a Point Charge in a Magnetic Field
Trajectory in Constant Magnetic Field
•  Suppose charge q enters B field with velocity v as
shown below. What will be the path q follows?
B cannot change |v| of a charged particle.

⇒ B cannot change the kinetic energy of a charged particle.

B can only change the direction of a particle.
x x x x x x x x x x x x
x x x x x x x x x x x x B
v
x x x x x x x x x x x x
F
q
v F
R
9/21/10
glow of ionized gas
13
Motion of a Point Charge in a Magnetic Field
9/21/10
14
Period of Circular Motion
The period of the motion is
or, the angular frequency
9/21/10
15
9/21/10
16
4
Mass Spectrometer (Ions with same KE)
• 
Mass Spectrometer (Ions with same KE)
Working with both equations :
The purpose of a mass spectrometer is to separate ions by mass and
measure the mass of each type of ion.
•  If positive ions start
from rest and move
through a potential
difference, V, the ions’
kinetic energy when
they enter the magnetic
field equals their loss in
potential energy:
First solve for the velocity on the first one,

v
Then substitute it on the kinetic energy equation
What kind of charge do the
ions in the picture have?
9/21/10
17
9/21/10
A mass spectrometer can be improved if instead of having
ions with the same kinetic energy entering the B field we
have ions with the same velocity.
18
5