1 Chapter 21
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1
Chapter 21
2
Hydrodynamics and Electromagnetism
Much of the terminology is the sameSome concepts can be applied between
the two fields
3
Amber
4
Charging By Induction
5
Two Things You Already Knew
1. Opposite charges attract
2. “Like” charges repel
6
Remembering Gravitation
Newton’s Law of Gravitation
rr
mGmF ˆ
221
7
What is Mass?
“resistance to acceleration”More fundamentally, a physical property
of matter In large quantity, groups of matter seem to
be always attracted to one another
Personally, I’d say “mass” is a lot weirder than “charge”
8
What is charge?
Physical property of matterTwo flavors: “plus” and “minus”
9
What is the smallest charge possible?
Millikan Oil Drop Experiment In 1910, Millikan was able to measure the
charge of the electron Recall: Atom made up of nucleus and clouds of
electrons outside nucleus Recall: nucleus: made up of protons and neutrons.
Protons have charge equivalent to electrons. Neutrons are neutral
Smallest charge possible is 1.602 x 10-19 Coulombs (C) aka e
10
Definition of Coulomb
Abbreviation: CAmount of charge through a cross-
section of wire in 1 second when there is 1 Ampere (A) of current.
(We’ll cover the amp later)
11
Okay, Mr. Smartguy, what about these quark-things?
Quarks– particles which make up the proton and neutron
The “up” quark has charge of +2/3 eThe “down” quark has charge of -1/3 eThey don’t count because there are no
“free” quarks. They always are confined in a particle
Proton- uud Neutron-udd
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Fundamental ParticlesParticle Symbol Charge in units of e
Electron e, e- , - -1
Proton p +1
Neutron n 0
Anti-electron (positron) - +1
Anti-proton -1
Anti-neutron 0
Alpha particle or 4He++ +2
Up quark u +2/3
Down quark d -1/3
Any element of atomic number, z
ZNX z
np
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How Charges Behave in materials
Conductors– charges move freelyInsulators—charges cannot move easilySemiconductors—charges only move
freely when certain conditions are met (heat, sufficient voltage, etc)
Superconductors-charges move effortlessly and cannot be stopped once they are moving
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Just like mass, charge is conserved
Energye
What is X?
HeThU X42
23423892
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Coulomb’s Law
Charles Augustin de Coulomb used a torsion pendulum to establish “Coulomb’s Law”
rr
qqkF ˆ
221
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k
k is equal to 1 for electrostatic units We use SI so in this case k is equal to
8.98 x 109 N·m2/C2
k is actually formed from two other constants
=3.1415928…. 0 = 8.854 x 10-12 C2/(N·m2)
Called the permittivity of free space
2
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0 C
mN109
4
1
k
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The product of q1and q2
If the product, q1q2 ,is negative then the force is attractive
If the product, q1q2 ,is positive then the force is repulsive
Your book uses the absolute value in the case of determining magnitude of force.
18
Where is r-hat?
The force is directed along the shortest distance between two points, just like gravitation.
In the case to the right, the force is directed along lines from the center of the spheres.
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1+1=2: The principle of superposition
Sometimes difficult problems can be made simple by using the principle of superposition.
Problem: Find the electric field of sphere with a hole in it.
= -
The E-field of the whole sphere
The E-field of a sphere with a hole in it
The E-field of a small sphere
The principle of superposition is one of the most powerful problem solving tools that you have
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At this point,
You should be able to work any of these force problems
Make a force diagramShow charges and locations
Use Coulomb’s law This is all Physics 250 stuff
NOW LET’S DO SOME PHYSICS 260!
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Electric Field
Why do I need this concept? Assume that you have a charge in space: we need a general
expression for when we add another charge, q. What force will be exerted on q?
Have I seen this before? Remember F=mg Our new expression: F=qE
E is the electric field that is present in the space wherein q was placed. E is usually the result of other charges which previously have been located in the same space.
Since E=F/q then the units are newtons per coulomb (N/C). Another set of units is volts per meter (V/m).
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A representation of earth’s gravitational field
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Electric Field Lines
Rules for Field Lines
1. Electric field lines point to negative charges
2. Electric field lines extend away from positive charges
3. Equipotential (same voltage) lines are perpendicular to a line tangent of the electric field lines
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Your Task
For the rest of this chapter and chapter 22, we will investigate how to calculate the electric field
rr
qkE ˆ
2
This quantity represents an infinite set of vector quantities, in other words, a vector field.
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The Problem
In order to calculate this quantity, we need to know how the charge creating the electric field is distributed in space
The geometrical distribution of the charge will have the biggest effect on the magnitude and direction of the electric field
rr
dqkEd ˆ
2
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4 Geometrical Situations-Point Charge
Point charge: All charge resides at a geometric point so there is no geometrical distribution
r-hat points out from the geometric point
rr
qkE
and
qdq
ˆ2
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4 Geometrical Situations-Line Charge
Line charge: All charge resides along a line
A charge density must be created: a mathematical description of the geometrical distribution of the charge
For a line charge, this is called the linear charge density, (units C/m)
2r
dskdE
and
dsdqds
dq
drds
drdds
dzordyordxds
2
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4 Geometrical Situations-Surface (or area) Charge
Surface charge: All charge resides on top or under a surface (or area)
surface charge density, (units C/m2)
2r
dakdE
and
dadqda
dq
dxdzordydzordxdyda
rdrda
rdrdda
2
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4 Geometrical Situations-Volume Charge
Volume charge: All charge resides in a particular volume
volume charge density, (units C/m3)
2r
dVkdE
and
dVdqdV
dq
dzrdrdzdrdrdV
drrdV
dddrrdV
dxdydzdV
2
4
sin2
2
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Electric Dipoles
A pair of charges, one “+” and the other “-” which are separated by a short distance
Electric dipole is represents the electrical distribution of many moleculesPositive and negative are relative concepts:
“positive” means less negative charges than “negative”
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Force and Torque on the Electric Dipole
Why is this important? Principle of microwave oven, amongst other applications
Recall: =r x F If F=qE, then =qE r sin ( where is the angle between E
and r) Let d=distance between two charges
Electric Dipole Moment Necessary because the charge and distance between
charges are easy to characterize p=qd Note: p is a vector in the direction pointing from 1
charge to the other =pE sinor =p x E
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Potential Energy
Recall that W=-UW=F·r=Fr cos=qEd cosU=-qd E cosU = - p·E which is the potential energy of
a dipole in an electric field
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