physics 72 chapter 21
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Electric Charge & Electric FieldChapter 21 of Young & Freedman’s
University Physics
1
Basic Laws/ Facts
1. Charge is conserved.
2. The electric field produced by a charge distribution is given by Coulomb’s Law.
3. Magnetic monopole or charge does not exist, while electric monopole or charge does exist.
4. A changing magnetic field produces an electric field.
5. The magnetic field is related to the currents, and to changing electric fields.
6. Electric and magnetic fields produces forces on charges according to the Lorentz equation.
We will devote about Sixty Days to study the ramifications of these Six Wisdoms.
http://images.allposters.com/images/30/007_yoda.jpg
2
Goals for the Day1. Discuss the dichotomy, quantization & conservation of
electric charge
2. Given the initial/final charge distribution, calculate the final/initial charge distribution using conservation principles
3. Predict charge distributions, & the resulting attraction or repulsion, in a system of charged insulators & conductors
4. Outline the process of charging
5. Calculate the net electric force on a point charge exerted by a system of point charges
3
Greeks, Amber & Wool
http://wikipedia/commons/6/68/Raffael_058.jpg; http://www.thebakken.org/electricity/images-static/amber-wool.jpg; http://en.wikipedia.org/wiki/Image:Gouttes-drops-resine-2.jpg; http://www.freewebs.com/fromagatetozoisite/Ambers.jpg; http://www.vision.smgroup.info/wp-content/uploads/2006/04/lamb.jpg
Elektron (Greek) = Amber (English) Electron
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Electron
Joseph John Thomson(1856 – 1940)
http://www.aip.org/history/electron/images/jj-equip.jpg; http://www.le.ac.uk/bs/em/images/sem_montage.jpg; http://www.engr.uky.edu/~bjhinds/facil/images/2010.jpg
Electron Microscope
Electron Microscope Images
5
Electric Charge Quantization
e = 1.602 x 10-19 Coulomb Neutron: 0 Proton: +e Electron: -e Nproton: total number of proton; integer Nelectron: total number of electron; integer Charge of an object, q = Nproton *(+e) + Nelectron*(-e)
Dichotomy positive (+) & negative (-) Positively charged object: Nproton > Nelectron
Negatively charged object: Nproton < Nelectron
Uncharged/neutral object: Nproton = Nelectron
Conservation of Electric Charge Charge is NOT created nor destroyed Charge is only transferred from one object to another Fundamental law of nature (like conservation of energy)
http://en.wikipedia.org/wiki/Image:Usdollar100front.jpg
Benjamin Franklin(1706 – 1790)
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Electric Charge: Interaction Positively charged object REPELS another
positively charged object
Negatively charged object REPELS another negatively charged object
Positively charged object ATTRACTS negatively charged object
Uncharged/neutral object ATTRACTS charged (positive or negative) object
http://www.pbs.org/kcet/wiredscience/education/wired,megavolt1.JPG; http://www.glenbrook.k12.il.us/gbssci/Phys/Class/estatics/u8l1c1.gif
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Like charges repel…Opposite charges attract…
but…
Why do protons not repel each other in the nucleus?Why do electrons not collapse into the nucleus?
Classical Electromagnetism CANNOT explain the structure of the atom…Quantum Mechanics can…
Classical Electromagnetism only explains phenomena at scales greater than 10-10 meters.
Wait a minute!!! Contradictions?...
r ≈1 Angstrom≈10-10 meters
8
Kinds of Materials: Insulator
Insulators: electrons are bound to a nearby nucleus;
electrons are not free to move about the entire material
9
Kinds of Materials: Conductor
Conductors: electrons are free to move about the entire material
10
Kinds of Materials
http://www.ntsb.gov/events/twa800/crossect.jpg; http://www.billfrymire.com/gallery/webJpgs/bounce-rubber-band-ball-elastic.jpg; http://en.wikipedia.org/wiki/Image:The_Earth_seen_from_Apollo_17.jpg ; http://www.friedlandindustries.com/images/new/NonferrousMetalsCopper.jpg; http://www.liquidsculpture.com/images/water/water-drop-a.jpg
copper (conductor)
rubber (insulator)
wood (insulator)
glass (insulator)water (conductor)
electric cable (conductor within an insulator)
Earth/ground (conductor)
11
Kinds of Materials
Semiconductor Conductivity is dependent on the
applied voltage Conducting at certain voltages;
insulating at other voltages
Superconductors Conductivity is perfect at certain
temperature & below (very, very cold temperature)
Cannot be explainable by Classical Electromagnetism
http://www.cstl.nist.gov/div837/Division/images/semi3.gif; http://www.chemistryland.com/CHM107/AirWeBreathe/Comp/superconductor2.jpg
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ChargingBasic ideas: Charge is conserved.Charging = add/remove charge to /from an object.Mechanically add or remove (rubbing an object with another charged object).Apply electric force (repel or attract) and allow the repelled charge to conduct to somewhere else.
Ground - a very large conductor that can supply an unlimited amount and kind of charge (e.g. earth).
Earth/ground
13
Charging
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l2b.html
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http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l2b.html
Charging15
Charging16
Charging: Electroscope
Electroscope: device for detecting electric charge
17
Electric Force: Coulomb’s Law
http://en.wikipedia.org/wiki/Image:Coulomb.jpg
Charles-Augustin de Coulomb1736 – 1806
The electrostatic force, F, between two point electric charges, q1 and q2, is directly proportional to the product, *, of the magnitudes of each charge and inversely proportional to the square
of the distance, r, between the charges.
F = k q1 * q2 ř12
r212
= k (±N1 e) * (±N2 e) ř12
r212
k (proportionality constant) = 1 ≈ 9 x 109 Nm2/C2
4πεo
εo (permittivity of free space) ≈ 8.85 x 10-12 C2/Nm2
18
Recall Newton’s Gravitational Law?
http://www.crystalinks.com/newton.jpg
Isaac Newton1642 – 1726
The electrostatic force, F, between two point masses, m1 and m2, is
directly proportional to the product, *, of the magnitudes of each charge and inversely proportional to the square
of the distance, r, between the masses.
F = G m1 * m2 ř12
r212
G (gravitational constant) = 6.67 x 10-11 Nm2/kg2
19
Force Vector quantity Depends on charge
Attractive or Repulsive Inverse square
Central; Weaker at greater distance Can act through vacuum Stronger than gravity Obeys Newton’s 3rd Law (Action-Reaction)
F12= - F21
Independent of geometrical & mechanical properties
Electric Force: Coulomb’s Law20
Principle of Superposition
The net force is the vector sum of all the individual forces acting on a system.
…in other words…
Consider two (test charge + another charge) at a time.
Apply Coulomb’s Law on each pair (as if other charges are not there).
Sum these pair-by-pair forces by vector addition.
21
Basic Electrostatic Problem
There is charge of interest (test), Q0 …
There is a group of charges…
What is the force exerted on Q0 by the other charges?
X
22
Basic Electrostatic ProblemTo determine whether they attract/ repel,
identify the magnitude & sign of the charges.
X
q1
Q0
q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Example:Q0 > 0 q1 > 0q2 < 0q3 < 0 q4 > 0etc…
23
Basic Electrostatic Problem
Calculate the distance between the other charges & Q0.
Example:r01 = distance bet. Q0 & q1 r02 = distance bet. Q0 & q2 r03 = distance bet. Q0 & q3 r04 = distance bet. Q0 & q4
etc…
X
q1
Q0
q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
24
Basic Electrostatic ProblemUse Coulomb’s Law on each pair.
X
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Q0
F01 = k Q0 * q1 ř01
r201
F02 = k Q0 * q2 ř02
r202
F03 = k Q0 * q3 ř03
r203
F04 = k Q0 * q4 ř04
r204
etc,…
25
Basic Electrostatic Problem
Get the net/total force, Fnet. Add the forces as vectors.
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Q0
F01 = F01xi + F01yjF02 = F02xi + F02yjF03 = F03xi + F03yjF04 = F04xi + F04yjetc,…
Fnet = F01 + F02 + F03 + F04 +…Fnet = (F01x+F02x+F03x+F04x+…)i + (F01y+F02y+F03y+F04y+…)j
Note the arrow heads (recall Q0 > 0; q1 > 0; q2 < 0; q3 < 0; q4 > 0; etc…)
Fnet on Q0
26
Basic Electrostatic Problem
X
q1
Q0
q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
http://www.earthsmightiest.com/images/news/animation/penguins2.jpg; http://uk.gizmodo.com/ChickenLittleSing.jpg
If you know vectors & vector addition, its chicken!
Vector: Magnitude & Direction
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Yes! Electric Fields…
Is there an alternative (better) approach to these problem?
28
http://images.art.com/images/-/LeBron-James--C10126004.jpeg; http://faculty.ssfs.org/~alisonb/Rodin%20Thinker-red.JPGhttp://www.tattonpark.org.uk/NR/rdonlyres/87A00E0B-9AAA-4852-82EF-9ADCC7137969/0/medievalcannon.jpg
How about the cannon ball?
Will the rubber ball go up?
29
http://www.earthsmightiest.com/images/news/animation/penguins2.jpg; http://uk.gizmodo.com/ChickenLittleSing.jpg
No! No!!! They will fall. They will fall.
…because of the earth’s “gravitational field”
30
What is a Field?
http://www.dkimages.com/discover/previews/740/51217.JPG
X
Go away, Blue Charge! Red Charge is mine.
Come here, Blue Charge.
I am in love.
FIELD… a quantity that has a value at each point in space; independent of the presence of object it acts on;
does not act on the object that produced it.
Action by CONTACT
31
What is a Field?
http://www.dkimages.com/discover/previews/740/51217.JPG
X
Go away, Chicken Little! Red Charge is mine.
Come here, Chicken Little.
I am in love.
FIELD… a quantity that has a value at each point in space; independent of the presence of object it acts on;
does not act on the object that produced it.
Anybody who stands here gets the attention of the
neighbors… especially of the Red Charge & Green Charge.
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“gravitational field” ↔ electric field
http://www.crystalinks.com/newton.jpg
Isaac Newton1642 – 1726
F = G m * Mearth ř12
R2earth
Charles-Augustin de Coulomb1736 – 1806
F = k Q0 * qother ř12
R20,other
g = G Mearth ř12
R2earth
F = m g
E = k qother ř12
R20,other
F = Q0 E
33
Basic Electrostatic Problem
There is charge of interest (test), Q’ …
There is a group of charges…
What is the force exerted on Q’ by the other charges?
X
34
Basic Electrostatic ProblemTo determine whether they attract/ repel,
identify the magnitude & sign of the charges.
X
q1
Q’
q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Example:Q’ > 0 q1 > 0q2 < 0q3 < 0 q4 > 0etc…
35
Basic Electrostatic Problem
Calculate the distance between the other charges & Q0.
Example:r01 = distance bet. Q’ & q1 r02 = distance bet. Q’ & q2 r03 = distance bet. Q’ & q3 r04 = distance bet. Q’ & q4
etc…
X
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Q’
36
Basic Electrostatic ProblemUse Coulomb’s Law on each pair.
X
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
Q’
F01 = k Q’* q1 ř01
r201
F02 = k Q’ * q2 ř02
r202
F03 = k Q’ * q3 ř03
r203
F04 = k Q’ * q4 ř04
r204
etc,…
37
Basic Electrostatic Problem
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
E01 = k q1 ř01
r201
E02 = k q2 ř02
r202
E03 = k q3 ř03
r203
E04 = k q4 ř04
r204
etc,…
38
Basic Electrostatic Problem
Get the net/total electric field, Enet. Add them as vectors.
q1q2 q3 q6 q8
q7
q4
q5
q10
q9
q11q12 q13
E01 = E01xi + E01yjE02 = E02xi + E02yjE03 = E03xi + E03yjE04 = E04xi + E04yjetc,…
Enet = E01 + E02 + E03 + E04 +…Enet = (E01x+E02x+E03x+E04x+…)i + (E01y+E02y+E03y+E04y+…)j
Note the arrow heads (recall Q0 > 0; q1 > 0; q2 < 0; q3 < 0; q4 > 0; etc…)
Enet at this point
39
Vocabulary Check: “Electrostatic”
ALL charge/ charge distribution has its corresponding electric field…
“Electrostatic” means…a situation where we assume that…
Electric field of the charge of interest (test charge) does not change the configuration of the other charges.
40
Basic Electrostatic Problem
We are not interested at charge of interest (test), Q’… unless it is there
There is a group of charges…
What is the Electric Field at that position?
41
Electric Field Calculations
(at this point)
(at this point)
(at this point)
42
Compute the ratio of the electric force to the gravitational force exerted by a proton on an electron in a hydrogen atom.
43
Three point charges lie on the x - axis; q1= 25nC is at the origin, q2 = -10nC is at x = 2m, and q0 = 20nC is at x = 3.5m. Find the net force on q0 due to q1 & q2.
44
Charge q1 = +25nC is at the origin, charge q2 = -15nC is on the x-axis at x = 2m,and charge q0 = +20nC is at the point x = 2m,y = 2m as shown. Find the resultant force F on q0.
45
46
47
When a test charge, q0 = 5nC, is placed at a certain point, it experiences a force Fnet = 2 × 10−4 N in the x-direction. What is the electric field E at that point?
What is the force, Fnet, on an electron placed at a point where the electric field is E = (4 × 10+4 N/C)i? (e ≈ 1.6 x × 10-19 C)
E = Fnet / q0= [(2 × 10−4 N)i]/(5 × 10−9 C) = 4 × 104 N/C)i
Fnet = q0E = (1.6 × 10−19 C)(4 × 10+4 N)i = (6.4 × 10-15 N)i
48
A positive charge q1 = +8nC is at the origin, and a second positive charge q2 = +12nC is on the x-axis at a = 4m. Find the net electric field (a) at point P1 on the x-axis at x = 7m, and (b) at point P2 on the x-axis at x = 3m.
49
A charge q is at x = a and a second charge -q is at x = a. Find the electric field on the x-axis at an arbitrary point x > a. (b) Find the limiting form of the electric field for x >> a.
50
Electric Field Calculations: Discrete Charges
You will need Algebra & Trigonometry
(at this point)
(at this point)
(at this point)
51
Electric Field Calculations: Continuous Charges
Now, you will need Calculus & Trigonometry.
Isaac Newton(invented Calculus)
(at this point)
(at this point)
(at this point)
52
Electric Field Calculations
line
surface
volume
53
Charge Densities
1 unit length
1 unit length
1 unit length
1 unit length
1 unit length
1 unit
length
linear charge density
surface charge density
volume charge density
54
E on the Axis of a Finite Line Charge
55
E off the Axis of a Finite Line Charge 56
E off the Axis of an Infinite Line Charge
inverse linear distance dependence
57
E on the Axis of a Ring Charge 58
E on the Axis of a Uniformly Charged Disc
E due to an Infinite Plane of Charge
no distance dependence
59
Electric Field Lines
Electric field lines begin on positive charges (or at infinity) & end on negative charges (or at infinity).
The lines are drawn symmetrically entering or leaving an isolated charge.
60
Electric Field Lines
Number of lines leaving a positive charge or entering a negative charge is proportional to the charge magnitude.
Density of the lines (number of lines /unit area perpendicular to the lines) at any point is proportional to the magnitude of the field at that point.
61
Electric Field LinesAt large distances from a system of charges, the field lines are equally spaced & radial, as if they came from a single point charge equal to the net charge of the system.
Field lines do not cross. (If two field lines crossed, that would indicate two directions for the electric field at the point of intersection.)
62
Electric Dipole
Two (2) charges [two “di”; charges poles] same magnitude, qopposite signclose (bound) together
- +d
+q-q
63
Electric Dipole: Dipole Moment
- +d
+q-q
64
p = qdDipole Moment, P vector (arrow: from - to +)“resistance” to turning/rotation
E
Dipole in a Uniform Electric Field: Forces & Torque
- ++++++++
-------
But if it has an angle it will turn TORQUE
ZERO (0) Net Force same magnitude opposite sign
-+ +-
65
Dipole in a Uniform Electric Field: Forces & Torque
- ++++++++
-------
TORQUE, τ
same magnitude opposite sign
/Fon - /= /Fon + / = FFon - - Fon + = Fnet = 0
τ = 2F(d/2)sinΘ = qEdsinΘ = qdEsinΘτ = qdEsinΘ = p x E
E
66
Dipole in a Uniform Electric Field: Potential Energy
Equilibrium (stable): Uminimum
-+ +-
67
-+
Dipole Potential Energy U = -p ∙ E
Umaximum = -(-p0) ∙ E = +p0 ∙ E
U = -p ∙ E = -p0EcosΘ;
/cosΘ/>0
Uminimum = -(p0) ∙ E= -p0E
p = qd
Ed on the x-axis at an arbitrary point x > a.
Electric Field of a Dipole, Ed
- +d
+q-q
a=d/2
The limiting form of Ed for x >> a.
Ed, at x>>a
Note: Ed is different from E shown in the previous slide. Ed is the field of the dipole.E is the field acting on the dipole.
68
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