Textbook Physics for Scientists and Engineers with Modern Physics Third Edition Pearson Education Inc. Fishbane/Gasiorowicz/Thornton Fundamentals of Physics Sixth Edition John Wiley & Sons. 2003 Halliday/Resnick/Walker References 大大大大大大 大大大大大 大大大大大大大
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Textbook Physics for Scientists and Engineers with Modern Physics Third Edition Pearson Education Inc. Fishbane/Gasiorowicz/Thornton Fundamentals of Physics.
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Textbook
Physics for Scientists and Engineerswith Modern Physics
Third Edition Pearson Education Inc.
Fishbane/Gasiorowicz/Thornton
Fundamentals of Physics
Sixth Edition John Wiley & Sons. 2003 Halliday/Resnick/Walker
References
大学物理教程 吴锡珑主编 高等教育出版社
Grading
Midterm exam 40
Final exam 50
Homework* 10
The homework must be completed before 8 o’clock on every Tuesday morning.
• have a solid conceptual understanding of the fundamental physical laws
• know how these laws can be applied to solve many problems
• know how physics is relevant to the world around us
Chapter 19 The Effects of Magnetic Fields
•Magnetic effects from natural magnets have been known for a long time.
•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. .
•Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.
•Bar magnet ... two poles: N and S Like poles repel; Unlike poles attract
•Small sliver of lodestone suspended with a string will always align itself in a north-south direction —it detects the earth’s magnetic field.
o5.11
19-1 Magnets and Magnetic Fields
Like poles repel Opposite poles attract
Forces between bar magnets
Magnet Magnetic Field Magnet
Magnetic fields can be mapped out using iron filings
Magnetic fields
Iron filings map the field of a horseshoe magnet
Magnetic field lines (defined in same way as electric field lines, direction and density)
a straight bar magnet a horseshoe magnet a current-carrying wire
The direction of the magnetic field of a magnet is from the north pole to the south pole
TABLE Some Approximate Magnetic Fields (T)
At the surface of a neutron star 108
Near a big electromagnet 1.5
Near a small bar magnet 10-2
At Earth's surface 10-4
In interstellar space 10-10
Smallest value in a magnetically shielded room 10-14
SI unit of tesla (T)
Electric Field Linesof an Electric Dipole
Magnetic Field Lines of a Bar Magnet
Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge).
How can you isolate this magnetic charge?
Even an individual electron has a magnetic dipole
Suppose we break a bar magnet
Each fragment becomes a separate magnet with its own north and south poles.
Magnetic monopoles do not exist (as far as we know).
19-2 Magnetic Force on a Point Charge
Experiment result
BqF
v
qB
vθ
We know about the existence of magnetic fields by their effect on moving charges. The magnetic field exerts a force on the moving charge.
F
The Lorentz Force
The force on a charge q moving with velocity through a region of space with electric field and magnetic field is given by:
A Notation for Vectors Perpendicular to the Page
ACT Two protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons. What is the relation between the magnitudes of the forces on the two
protons?
(a) F1 < F2 (b) F1 = F2 (c) F1 > F2 B
x
y
z
1
2
v
v
(a) F2x < 0 (b) F2x = 0 (c) F2x > 0
What is F2x, the x-component of the force on the second proton?
(a) decreases (b) increases (c) stays the same
Inside the B field, the speed of each proton:
19-3 Consequences of the Magnetic Force on a Charge
A static magnetic field does no work on a charge
Circular Motion in a Constant Magnetic Field
• Bv
qB
mR
v
B
qv
What will be the path q follows?Path will be circle
F
qB
mRT
22
v m
qBf
2
The period and frequency
The tracks left by charged particles moving through a bubble chamber in a magnetic field
The frequency of the circular motion does not depend on the speed (application: Cyclotron)
• Bv
B
//v
v
h
The path of the particle is a helix
v
The radius
The pitch(inclination)
A charged particle follows a helical path in a region where the magnetic field is constant.
An electron in a cloud chamber produced this 10-m-long spiral track.
• Magnetic Focusing B
Particle source A
When is small enough
qBm
Thv
v 2
//
Receiver A'
After a period, the particle which has small deflection angle will focus again.
ACT The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure.
1) What is the direction of the magnetic field in chamber 1?
a) Up b) Down c) Left d) Right e) Into page f) Out of page
2) What is the direction of the magnetic field in chamber 2?
a) Up b) Down c) Left d) Right e) Into page f) Out of page
3) Compare the magnitude of the magnetic field in chamber 1 to the magnitude of the magnetic field in chamber 2.
a) B1 > B2 b) B1 = B2 c) B1 < B2
• The Cyclotron
a top view of the region of a cyclotron in which the particles (protons) circulate.
A uniform magnetic field is directed up from the plane of the page. Circulating protons spiral outward within the hollow dees, gaining energy every time they cross the gap between the dees
m
qBfosc 2
Applications
• Velocity Selector
A particle moving in a region where there are both electric and magnetic fields can experience no net force
Only particles of a specific velocity will cross the region undeflected
• Charge-to-Mass Ratio of the Electron
First accelerate electrons through a known potential difference V, and then adjust electric and magnetic fields so they are not deflected. Thomson’s Apparatus
Thomson (1897) measures q/m ratio for “cathode rays” All have same q/m ratio, for any material source.Electrons are a fundamental constituent of all matter!
N: ion sourceN: ion source
RR
+ -
PP
NN
BB
• Mass Spectrometer
P: velocity selector
B’
Deflection depends on mass:
Lighter deflects more, heavier less
Mass spectrometry is a technique for separating ions by their mass-to-charge (m/z) ratios
*Motion of a Point Charge in a Nonuniform Magnetic Field
Magnetic field can confines a charged particle spiraled around a field line.
B R
• Magnetic Confinement
B
A charged particle spiraling in a magnetic field, which is strong at both ends and weak in the middle, the particle becomes trapped and moves back and forth spiraling around the field lines.
• “Magnetic Bottle”
The Van Allen radiation belts
Electrons and protons are trapped by the magnetic field of Earth. They form the Van Allen radiation belts
When particles strike the upper atmosphere and fluoresce, causing the polar aurora.
Observers in different inertial frames see different combinations of electric and magnetic fields
The general transformation formula for special relativity are
From the example we know that it is totally relative to divide electromagnetic field into certain electric field and magnetic field.
19-4 The Hall Effect (1879)
When a conducting strip carrying a current is placed in a magnetic field, the magnetic force on the charge carriers causes a separation of charge called the Hall effect.
Experiment result
d
IBKVab
d
I
B
a
b
In equilibrium situation
Analysis
vl
d
I
B
a
+q
mf
+ + + +
– – – –ef
E
E
b
• Hall effect in hybrid semiconductors is used to distinguish experimentally between n-type and p- type materials.
B
+ + + +
– – – –a
b
ba VV
a
b
+ + + +
– – – –
ba VV 0K0K
I I
v
q
p-type
v
q
B
Discussion
• Hall effect is used to measure the number density of charge carriers in conductors or semiconductors.
n-type
nqd
IBVab
High temperature gas (plasm) B
• The Magnetohydrodynamic (MHD) Generator
• Magnetic field can be measured using Hall probe
19-5 Magnetic Forces on Currents
Currents consist of moving charges, so will experience force in magnetic field.
Magnetic Forces on Infinitesimal Wires with Currents
Consider a current-carrying wire in the presence of a magnetic field .
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 positive charges/volume each carrying charge q and moving with velocity v through a wire of cross-section A.
has the infinitesimal magnitude and the direction of the current
Magnetic Forces on Finite Wires with Currents
(3) For a straight wire of length L making an angle θ with the magnetic field:
We define the vector as having the length of the wire and the direction of the current
(1)
(2) For uniform magnetic field
In uniform magnetic field , the force acting on a current loop is
Discussion
BLIF
x
y
O A
I
L
B
For a current element lI
d
lI
dF
d
Example A wire of current I snakes along an arbitrary curved path in the x-y plane, A uniform magnetic field is perpendicular to the plane, find the total force on the wire.
Solution
The force on the wire is the same as that on a straight wire between O and A. The force is in the direction of y.
F
x
I
c d
Example A circular loop has radius R and carries current I in the clockwise direction. A magnetic field B exists in the negative z-direction. Find the tension in the loop.
y
Solution The force on a small segment
The net force on loop is 0
f
TT
Consider the upper half loop. The forces on it are f, TIt is in equilibrium.
CDF
ABF
Torque on current loops in a uniform magnetic field
B
1l
2l
DAF
BCF
D
CB
AI
the torque about the center axis
B
+n
A(B)
D(C)
19-6 Magnetic Force on Current Loops
Consider loop in magnetic fieldas on right
The net force on loop is 0. But there is a torque.
n
We can define the magnetic dipole moment of a current loop as follows:
direction:
magnitude:
Torque on loop can then be rewritten as:
Note: if loop consists of N turns
CDF
ABF
B
+n
A(B)
D(C)
Discussion
(1) The torque tends to increase the magnetic flux
stable equilibrium
(3) Current loops in non-uniform magnetic field
The loop will move and rotate.
B
+n
A(B)
D(C)
unstable equilibrium
(2) The equation also applies to non-rectangular loop
Electric Dipole Analogy
(per turn)
Bx
.
E
.
+q
-q
Bar Magnet Analogy
You can think of a magnetic dipole moment as a bar magnet:
– In a magnetic field they both experience a torque trying to line them up with the field
– We will see in the next chapter that such a current loop does produce magnetic fields, similar to a bar magnet. In fact, atomic scale current loops were once thought to completely explain magnetic materials (in some sense they still are!).
=N
S
Galvanometer
The galvanometer: a device that measures currents
The galvanometer uses the fact that a magnetic field exerts a toque on a current loop to measure currents:
– In this picture the loop (and hence the needle) experiences a torque
– The spring produces a countertorque
– The needle will sit at its equilibrium position
– A larger current means a larger torque
Galvanometers are at the heart of many ammeters and voltmeters.
Electric Motor
A current-carrying loop is placed in the magnetic field.
A split-ring commutator is used to change the direction of the current every time the loop passes 180o
The torque on the loop serves to turn the loop
Example A plastic disk with radius R1 and R2 is placed in the uniform magnetic field . The charge q is uniformly distributed on the disk. The disk rotates about its axis with .Find the magnetic dipole moment of the disk and the torque on the disk.
R1R2
Solution Consider a circular strip
B
+n
A(B)
D(C)
The work done by the magnetic force
The minus sign arises because the torque tends to decrease
Potential Energy of Dipole
The work depends only on position, we can introduce the potential energy.
Define a potential energy U with zero at position of max torque
A current loop in a magnetic field has potential energy, depending on the angle between µ and B .
B
x
Bx
B
x
= 0
U = -B
= 0
U = B
positive work negative work
=B
X
U = 0
stable unstable
ACT A circular loop of radius R carries current I as shown in the diagram. A constant magnetic field B exists in the +x direction. Initially the loop is in the x-y plane.
(c) It will not rotate
(1)The coil will rotate to which of the following positions?
I
R
x
y B
a b
a b
(a)x
y
(b)
a b
x
y
(a) U0 is minimum
(b) U0 is maximum
(c) neither
(2) What is the potential energy U0 of the loop in its initial position?
I
R
x
y B
a b
Example Figure below shows a circular coil with 250 turns, an area A of 2.52 * 10-4 m2, and a current of 100 A. The coil is at rest in a uniform magnetic field of magnitude B = 0.85 T, with its magnetic dipole moment initially aligned with .
(a) what is the direction of the current in the coil?
(b) How much work would the torque applied by an external agent have to do on the coil to rotate it 90° from its initial orientation, so that is perpendicular to and the coil is again at rest?
Solution
(a) applying the right-hand rule to the coil ,the direction of the current in the wires on the near side of the coil is from top to bottom.
(b) work done by an external agent
Example A rectangular wire loop of width a and height b is connected to a current source that, when turned on, gives rise to a current I in the wire. The loop is suspended in a uniform magnetic field that points in a vertical direction, and it would hang vertically if there were no current. We assume that the wire is massless, but two masses m are suspended at the lower corners. What is the angle at which the loop is in equilibrium? What happens if the direction of the current is reversed?
Solution
The magnetic dipole moment
At equilibrium, the net torque is zero
if the direction of the current is reversed, the loop will rise to the same angle on the other side of the vertical
pivot
b
2mg
Another way :
Use the condition of the minimal potential energy at equilibrium
Choose the vertical plane as the reference position for the potential energy