Download Lecture 09 - Purdue Physics

PHYS 221 General Physics II
Magnets, Magnetic Fields
Spring 2015
Assigned Reading: 20.1 – 20.4
Lecture 9
Review: RC Circuit
In the process of charging,
the voltage on capacitor
changes as:
Vc (t)   (1 e
t /
)
In the process of
discharging, the voltage
on capacitor changes as:
Vc (t)   e
Phys 221 Spring 2014
t /
Lecture 09
2
Ammeters
• An ammeter is a device
that measures current.
• An ammeter must be
connected in series with
the desired circuit branch.
• An ideal ammeter will
measure current without
changing its value.
– Must have a very low
resistance.
Phys 221 Spring 2014
Lecture 09
3
Voltmeters
•
A voltmeter measures the
voltage across a circuit
element.
•
It must be connected in parallel
with the element of interest.
•
An ideal voltmeter should
measure the voltage. without
changing its value.
– The voltmeter should have
a very high resistance.
Phys 221 Spring 2014
Lecture 09
4
Magnetic Field
•
•
•
Phys 221 Spring 2014
Lecture 09
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
5
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)
N
S
S
N
N
N
S
S
Attraction
Repulsion
From North to South outside
From South to North inside
Always close on themselves
Phys 221 Spring 2014
Lecture 09
6
Magnetic Field
• The magnetic poles are indicated
at the ends of the bar magnet
– Called north and south
• The magnetic poles are
analogous to positive and
negative charges
• The north poles of the filings are
attracted to the south pole of the
bar magnet
• Magnetic field lines form closed
loops.
Phys 221 Spring 2014
Lecture 09
7
DEMO of Magnetic Field Lines
Electric Field Lines
of an Electric Dipole
+
-
Magnetic Field Lines of a
bar magnet
Phys 221 Spring 2014
Lecture 09
8
i>Clicker question
A
Which drawing shows the correct
field lines for a bar magnet?
(A)
(B)
S
N
S
N
S
N
B
(C)
C
Phys 221 Spring 2014
Lecture 09
9
Horseshoe Magnet
• It can be made by
bending a bar
magnet.
• There are poles at
the ends of the
horseshoe.
• The field is largest in
the horseshoe gap.
• The field is directed
across the gap.
Phys 221 Spring 2014
Lecture 09
10
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 but scientists are looking for
them.
Phys 221 Spring 2014
Lecture 09
11
Magnetic Force on a Moving Charge
The force F on a charge q moving with velocity
v through a region of space with a magnetic
field B is given by:
Phys 221 Spring 2014
Lecture 09
12
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 is never parallel to v.
FB can only change the direction of the particle not the speed.
Phys 221 Spring 2014
Lecture 09
13
More on Magnetic Force
• 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 SI unit for magnetic field is tesla (T):
-4
A common unit gauss (G): 1 G = 10 T
Phys 221 Spring 2014
Lecture 09
~Earth’s surface
field!
14
The Magnetic Force

 
F

q
v

B

The direction of the force is:
B
B
x x x x x x
x x x x x x
v
v
v
x x x x x x
FB
B
+q
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
x x x x x x x x x x x x
v
Phys 221 Spring 2014
F
F
Lecture 09
B
q
15
Motion in Uniform Magnetic Field
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.
Phys 221 Spring 2014
Lecture 09
glow of ionized gas
16
i>Clicker question
Each chamber has a unique
magnetic field. A positively
charged particle enters chamber
1 with velocity 75 m/s up, and
follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 2?
A. up
B. down
C. left
D. right
E. into page
F. out of page
Phys 221 Spring 2014
Lecture 09
17
Trajectory in Constant Magnetic Field
• Suppose charge q enters B field with velocity v as
shown below. What will be the path q follows?
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
v
F
F
q
R
Phys 221 Spring 2014
Lecture 09
18
Motion in Uniform Magnetic Field
• Assume a charged particle
moves perpendicular to the
magnetic field.
• The angle between the
velocity and the field is 90°.
• Therefore, the force is qvB.
• The particle will move in a
circle.
• The circle lies in the plane
perpendicular to the
magnetic field lines.
Phys 221 Spring 2014
Lecture 09
19
Motion of a Point Charge in a Magnetic Field

 
FB  qv  B



If v is  B then FB  qvB
FB  ma  qvB
Charge follows uniform circular motion
thus there is a centripetal force on the
charge
mv 2
Fc 
r
The only force acting on the charge is the magnetic
mv 2
 qvB
r
Phys 221 Spring 2014
mv
r
qB
Lecture 09
20
Period of Circular Motion
The period of the motion is
2r 2 mv 2m
T


v
v qB qB
Called the
cyclotron
period.
or, the angular frequency
2 qB
  2f 

T
m
only a function of q/m, but not the velocity v!
Larger v: circumference grows IN PROPORTION
Phys 221 Spring 2014
Lecture 09
21
Mass Spectrometer
• Allows for the separation
of ions according to their
mass or charge.
• The ions enter with some
speed v.
• They pass into a region
where the magnetic field
is perpendicular to the
velocity.
• The ions travel in a circle
in the mass spectrometer.
Phys 221 Spring 2014
Lecture 09
22
Mass Spectrometer
• The radius of the circle is mv/qB.
– Ions with different masses will travel in arcs with
different radii.
• Mass spectrometer can also be used to find the
composition of a material.
– Measure the values of v, B and r.
– Calculate charge-to-mass ratio, q/m.
Phys 221 Spring 2014
Lecture 09
23
Helical Motion
• Assume a charged
particle moves neither
parallel nor
perpendicular to the
magnetic field.
• The angle between the
velocity and the field
varies.
• The path of the particle
is helical.
– The charged particle
will spiral around the
magnetic field lines.
Phys 221 Spring 2014
Lecture 09
24
Summary: Motion of a Charged Particle
• If a charged particle has a velocity parallel to the
magnetic field, the magnetic force on the particle is
zero.
• If a charged particle is moving perpendicular to a
constant magnetic field, the particle will move in a
circle.
• If a charged particle is moving with a velocity at some
angle between 0°and 90°, it will spiral around the
magnetic field lines.
Phys 221 Spring 2014
Lecture 09
25