PHY127 Summer Session I I. Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-0 8. The website above is the point of contact outside the class for important messages, so regularly and frequently check the website. - PowerPoint PPT Presentation
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PHY127 Summer Session II Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08 homework problems for each chapter are in general due a week 11:59 pm and are delivered through MasteringPhysics website tp://www.masteringphysics.com. You need to open an account. addition to homework problems, there is naturally a reading quirement of each chapter, which is very important. website above is the point of contact outside the class for i ages, so regularly and frequently check the website. end of class a quiz is given for the previous chapter covere ass. Bring a calculator (no wireless connection), a pencil, copy of lecture note for the chapter. lab session is an integrated part of the course and make sure will attend all the sessions. See the syllabus for the detail rmation and the information (e.g. lab manuals) at the website
Transcript
PHY127 Summer Session II• Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08
• 5 homework problems for each chapter are in general due a week later at 11:59 pm and are delivered through MasteringPhysics website at: http://www.masteringphysics.com. You need to open an account.
• In addition to homework problems, there is naturally a reading requirement of each chapter, which is very important.
• The website above is the point of contact outside the class for important messages, so regularly and frequently check the website.• At the end of class a quiz is given for the previous chapter covered in the class. Bring a calculator (no wireless connection), a pencil, an eraser, and a copy of lecture note for the chapter.• The lab session is an integrated part of the course and make sure that you will attend all the sessions. See the syllabus for the detailed information and the information (e.g. lab manuals) at the website above.
Chapter 20: Electric Charge/Force/Field
Electric charge
Two opposite signed charges attract each other
Two equally signed charges repel each other
When a plastic rod is rubbed with a piece of fur, the rod is “negatively” charged
When a glass rod is rubbed with a piece of silk, the rod is “positively” charged
Electric charge is conserved
Electric charge (cont’d)
Particle Physics
Model of Atoms
electrons e-
nucleus
Old view
Semi-modern view
Modern view
nucleusquarks
prot
on
What is the world made of?
Electric charge (cont’d)
• Electron: Considered a point object with radius less than 10-18 meters with electric charge e= -1.6 x 10 -19 Coulombs (SI units) and mass me= 9.11 x 10 -
31 kg
• Proton: It has a finite size with charge +e, mass mp= 1.67 x 10-27 kg and with radius– 0.805 +/-0.011 x 10-15 m scattering experiment– 0.890 +/-0.014 x 10-15 m Lamb shift experiment
• Neutron: Similar size as proton, but with total charge = 0 and mass mn=– Positive and negative charges exists inside the neutron
• Pions: Smaller than proton. Three types: + e, - e, 0 charge.– 0.66 +/- 0.01 x 10-15 m
• Quarks: Point objects. Confined to the proton and neutron,– Not free– Proton (uud) charge = 2/3e + 2/3e -1/3e = +e– Neutron (udd) charge = 2/3e -1/3e -1/3e = 0– An isolated quark has never been found
Electric charge (cont’d)
Electric charge (cont’d)
• Two kinds of charges: Positive and Negative• Like charges repel - unlike charges attract• Charge is conserved and quantized
1. Electric charge is always a multiple of the fundamental unit of charge, denoted by e.
2. In 1909 Robert Millikan was the first to measure e.Its value is e = 1.602 x 10−19 C (coulombs).
3. Symbols Q or q are standard for charge.4. Always Q = Ne where N is an integer5. Charges: proton, + e ; electron, − e ; neutron, 0 ; omega, − 3e ;
quarks, ± 1/3 e or ± 2/3 e – how come? – quarks always exist in groups with the N×e rule applying to the group as a whole.
Charging by contact
Charging by induction (cont’d)
Conductors, insulators, and induced charges
Conductors : material in which charges can freely move. metal Insulators : material in which charges are not readily transported. wood Semiconductors : material whose electric property is in between. silicon Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges
Coulomb’s law
Coulomb’s law- The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them
221
rqq
kF r : distance between two chargesq1,q2 : chargesk : a proportionality constant
- The directions of the forces the two charges exert on each other are always along the line joining them.- When two charges have the same sign, the forces are repulsive.- When two charges have opposite signs, the forces are attractive.
+ +r
q1 q2
- -r
q1 q2
+ -r
q1 q2
F2 on 1 F1 on 2 F2 on 1 F1 on 2 F1 on 2F2 on 1
Coulomb’s law
Coulomb’s law and units
221
rqq
kF r : distance between two charges (m)q1,q2 : charges (C)k : a proportionality constant (=ke)
229
229
229
C/mN100.9
C/mN10988.8
C/mN10987551787.8
k
s/m102.99792458c 8
)mN/(C10854.8;4
1c)C/sN10(
22120
0
2227
k
SI units
Exact by definition
C10)63(602176462.1 19echarge of a proton
C10nC1 -9
Coulomb’s law
Example: Electric forces vs. gravitational forces
2
2
041
rqFe
2
2
rmGFg
electric force
gravitational force
+ +r
q q
35
227
219
2211
229
2
2
0
101.3
)kg1064.6(C)102.3(
kg/mN1067.6C/mN100.9
41
mq
GFF
g
e
Gravitational force is tiny compared with electric force!
kg1064.6
102.3227
19
m
Ceq
+ +0
0protonneutron
particle
Coulomb’s law
Example: Forces between two charges
1on2
2
9-9229
221
02on1
N 019.0m)030.0(
C)10C)(751025()C/mN100.9(
41
F
rqq
F
nC75nC,25 21 qq
+ -r
F1 on 2F2 on 1
cm0.3r
1on22on1 FF
Coulomb’s law
Superposition of forces Principle of superposition of kforces
When two charges exert forces simultaneously on a third charge,the total force acting on that charge is the vector sum of the forcesthat the two charges would exert individually.
Example: Vector addition of electric forces on a line
+ -2.0 cm
F1 on 3F2 on 3
+
q1q2q3
4.0 cm
Coulomb’s law
Example: Vector addition of electric forces in a plane
N29.0m)50.0(
C)10C)(2.0100.4()C/mN100.9(
41
2
6-6229
21
1
01
QQon r
QqF
+
+
+
0.50 m
0.50 m
0.40 m0.30 m
0.30 m
q1=2.0 C
q2=2.0 C
Q=4.0 C
QonF1
xQonF )( 1
yQonF )( 1
N23.00.50m0.40mN)29.0(cos)()( 11 QonxQon FF
N17.00.50m0.30mN)29.0(sin)()( 11 QonyQon FF
0N17.0N17.0N0.460.23NN23.0
y
x
FF
force due to q2
Electric field and electric forces
Electric field and electric forces
++ +
++++
++
A B
0F
0F
0q+ +
++++
++
A
P
remove body B
•Existence of a charged body A modifies property of space and produces an “electric field”. •When a charged body B is removed, although the force exerted on the body B disappeared, the electric field by the body A remains. •The electric force on a charged body is exerted by the electric field created by other charged bodies.
Electric field and electric forces
Electric field and electric forces (cont’d)
+ ++
+++++
A Test charge
0F
0F
0q+ +
++++
++
A
P
placing a test charge
• To find out experimentally whether there is an electric field at a particular point, we place a small charged body (test charge) at point.• Electric field is defined by
0
0
qFE
(N/C in SI units)
• The force on a charge q: EqF
Electric field and electric forces
Electric field of a point charge
+ -
rrr /ˆ
r̂ r̂P P
q0 q0
q q
S S
E
E
20
00 4
1r
qqF
0
0
qFE
+
rrqE ˆ
41
20
+
r̂ P
q0
q
S
E
'E
P’
'r̂
'' EErr
Electric field and electric forces Electric field by a continuous charge distribution
q
Electric field and electric forces Electric field by a continuous charge distribution (cont’d)
These may be considered in 1, 2 or 3 dimensions.
There are some usual conventions for the notation:
Charge per unit length is λ ; units C/m i.e, dq = λ dl
Charge per unit area is σ ; units C/m2 i.e, dq = σ dA
Charge per unit volume is ρ ; units C/m3 i.e, dq = ρdV
Electric field and electric forces
Example : Electron in a uniform fieldy
xO
1.0 cm -E
-
+
100 V
Two large parallel conducting plates connected to a battery produce uniform electric field N/C1000.1 4E Since the electric force is constant, the acceleration is constant too
EeF
21531
419
m/s1076.1kg1011.9
N/C)10C)(1.001060.1(
meE
mF
a yy
From the constant-acceleration formula: )(2 020
2 yyayyy
0,0m/s109.52 00y6 yyayy when cm0.1y
The electron’s kinetic energy is: J106.1)2/1( 172 mK
The time required is: sa
ty
yy 90 104.3
Electric field lines An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric-field vector at that point.
Electric field lines show the direction of at each point, and their spacing gives a general idea of the magnitude of at each point.
E
E
Where is strong, electric field lines are drawn bunched closely together; where is weaker, they are farther apart.
E
E
At any particular point, the electric field has a unique direction so that only one field line can pass through each point of the field. Field lines never intersect.
Electric field lines
• E-field lines begin on + charges and end on - charges. (or infinity)
• They enter or leave charge symmetrically.• The number of lines entering or leaving a
charge is proportional to the charge.• The density of lines indicates the strength
of E at that point.• At large distances from a system of charges,
the lines become isotropic and radial as froma single point charge equal to the net chargeof the system.
• No two field lines can cross.
Field line drawing rules: Field line examples
Electric field lines (cont’d) Field line examples (cont’d)
Electric Dipoles An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d.
q qqd
d
electric dipole moment
Water molecule and its electric dipole
Electric Dipoles Force and torque on an electric dipole
q
q
EqF
EqF
)sin)(( dqEqdp
Ep
torque:electric dipole moment:
work done by a torque during an infinitesimal displacement d
dpEddW sin
Electric Dipoles Force and torque on an electric dipole (cont’d)
q
q
EqF
EqF
)(
coscos)sin(
12
122
1
2
1
UU
pEpEdpEdW
EppEU
cos)(potential energy for a dipolein an electric field
Exercises Trajectory of a charged particle in a uniform electric field
Exercises Cathode ray tube
Exercises Electric field by finite line charge
Exercises Electric field by a ring charge
Exercises Electric field by a uniformly charged disk
Exercises Electric field by infinite plate charge
+++++++
Exercises Electric field by two oppositely charged parallel planes
