PHY127 Summer Session II • Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08 • 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. • 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.
Transcript
PHY127 Summer Session II• Most of information is available at:http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08
• The website above is the point of contact outside the class for importantmessages, so regularly and frequently check the website.
• At the end of class a quiz is given for the previous chapter covered inthe 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 thatyou will attend all the sessions. See the syllabus for the detailedinformation and the information (e.g. lab manuals) at the website above.
• 5 homework problems for each chapter are in general due a week laterat 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 readingrequirement of each chapter, which is very important.
Chapter 20: Electric Charge/Force/Field
Electric charge
Two opposite signed charges attract eachother
Two equally signed charges repel eachother
When a plastic rod is rubbed with a pieceof fur, the rod is “negatively” charged
When a glass rod is rubbed with a pieceof silk, the rod is “positively” charged
Electric charge is conserved
Electric charge (cont’d)
What is the world made of?
Electric charge (cont’d)Particle Physics
nucleusModel of Atoms
electrons e-
Old view
prot
on
nucleusquarksModern view
Semi-modern view
• 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 freelymove. metal
Insulators : material in which charges are notreadily transported. wood
Semiconductors : material whose electric property is in between. silicon
Induction : A process in which a donor materialgives opposite signed charges toanother material without losing any ofdonor’s charges
Coulomb’s law
Coulomb’s law- The magnitude of the electric force between two point chargesis directly proportional to the product of the charges and inverselyproportional to the square of the distance between them
r : distance between two chargesq1,q2 : chargesk : a proportionality constant2
21
rqq
kF =
- The directions of the forces the two charges exert on each otherare 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.
q2 q2 q2q1 q1 q1
+ + - - + -r r rF2 on 1 F1 on 2 F2 on 1 F1 on 2 F1 on 2F2 on 1
Coulomb’s law
Coulomb’s law and unitsr : distance between two charges (m)q1,q2 : charges (C)k : a proportionality constant (=ke)
221
rqq
kF =
229
229
229
C/mN100.9C/mN10988.8
C/mN10987551787.8
⋅×≅
⋅×≅
⋅×=k SI units
s/m102.99792458c 8×=
)mN/(C10854.8;4
1c)C/sN10(
22120
0
2227
⋅×==
⋅=
−
−
επε
k Exact by definition
C10)63(602176462.1 19−×=eC10nC1 -9=
charge of a proton
Coulomb’s law
Example: Electric forces vs. gravitational forces
2
2
041
rqFe πε
= q qkg1064.6
102.3227
19
−
−
×=
×=+=
mCeq
electric force
+ +r
2
2
rmGFg =gravitational force
+ +0
0
neutronproton α particle
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
πε
Gravitational force is tiny compared with electric force!
Coulomb’s law
Example: Forces between two charges
nC75nC,25 21 −=+= qq
cm0.3=r+ -r
F1 on 2F2 on 1
1on2
2
9-9229
221
02on1
N 019.0m)030.0(
C)10C)(751025()C/mN100.9(
41
F
rqq
F
==
××⋅×=
=
−
πε
1on22on1 FFrr
−=
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
q3 q2 q1F2 on 3+ -
F1 on 3+
2.0 cm
4.0 cm
Coulomb’s law
Example: Vector addition of electric forces in a plane
•Existence of a charged body A modifies property of space andproduces an “electric field”.
•When a charged body B is removed, although the force exerted onthe body B disappeared, the electric field by the body A remains.
•The electric force on a charged body is exerted by the electric fieldcreated by other charged bodies.
Electric field and electric forces
Electric field and electric forces (cont’d)A A Test charge
0qP
0Fr+ +
++++
++ + +
++++
++
0Fr
−placing a test charge
• To find out experimentally whether there is an electric field at aparticular point, we place a small charged body (test charge) atpoint.
0
0
qFEr
r=• Electric field is defined by (N/C in SI units)
EqFrr
=• The force on a charge q:
Electric field and electric forces
Electric field of a point charge
+ -
rrr /ˆ r=
r̂ P
q0
S
Er
Erq0
r̂P
S
q q
0
0
qFEr
r=2
0
00 4
1r
qqF
πε= +
+
r̂ P
q0
S
Er
'Erq 'r̂
'' EErrrr
<→>
rrqE ˆ
41
20πε
=r
P’
Electric field and electric forcesElectric field by a continuous charge distribution
q
Electric field and electric forcesElectric 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 -Er
-
+
EeFrr
−= 100 V
Two large parallel conducting plates connected to a battery produceuniform electric field N/C1000.1 4×=ESince the electric force is constant, the acceleration is constant too
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 −+=υυ
0,0m/s109.52 00y6 ==←×== yyayy υυ when cm0.1−=y
The electron’s kinetic energy is: J106.1)2/1( 172 −×== υmK
The time required is: sa
ty
yy 90 104.3 −×=−
=υυ
Electric field linesAn electric field line is an imaginary line or curve drawn
through a region of space so that its tangent at any pointis 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.
Er
Er
Where is strong, electric field lines are drawn bunchedclosely together; where is weaker, they are farther apart.
Er
Er
At any particular point, the electric field has a uniquedirection so that only one field line can pass through eachpoint of the field. Field lines never intersect.
Electric field lines Field line drawing rules: Field line examples
• 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.
Electric field lines (cont’d)Field line examples (cont’d)
Electric DipolesAn electric dipole is a pair of point charges with equalmagnitude and opposite sign separated by a distance d.
q qqd
d
electric dipole moment
Water molecule and its electric dipole
Electric DipolesForce and torque on an electric dipole
q
q
EqFrr
−=−
EqFrr
=+
φ
)sin)(( φτ dqE=qdp =
torque:electric dipole moment:
Eprrr
×=τwork done by a torque τduring an infinitesimal displacement dφ : φφφτ dpEddW sin−==
Electric DipolesForce and torque on an electric dipole (cont’d)
q
q
EqFrr
−=−
EqFrr
=+
)(
coscos)sin(
12
122
1
2
1
UU
pEpEdpEdW
−−=
−=−== ∫∫ φφφφφτφ
φ
φ
φ
φ
EppEUrr
⋅−=−≡ φφ cos)(potential energy for a dipolein an electric field
ExercisesTrajectory of a charged particle in a uniform electric field
ExercisesCathode ray tube
ExercisesElectric field by finite line charge
ExercisesElectric field by a ring charge
ExercisesElectric field by a uniformly charged disk
ExercisesElectric field by infinite plate charge
+++++++
ExercisesElectric field by two oppositely charged parallel planes
