Transcript Chapter 21: Electric Charge and Electric Field

Chapter 21
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Hydrodynamics and
Electromagnetism
Much of the terminology is the same
 Some concepts can be applied between
the two fields

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Amber
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Charging By Induction
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Two Things You Already Knew
1. Opposite
charges
attract
2. “Like” charges repel
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Remembering Gravitation

Newton’s Law of Gravitation
  Gm1m2
ˆ
F
r
2
r
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What is Mass?
“resistance to acceleration”
 More fundamentally, a physical property
of matter
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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”
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What is charge?
Physical
property of
matter
Two
flavors: “plus” and
“minus”
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What is the smallest charge
possible?

Millikan Oil Drop Experiment
 In 1910, Millikan was able to measure the
charge of the electron

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
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
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Definition of Coulomb
Abbreviation: C
 Amount of charge through a crosssection of wire in 1 second when there is
1 Ampere (A) of current.
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(We’ll cover the amp later)
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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 e
 The “down” quark has charge of -1/3 e
 They 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 Particles
Particle
Symbol
Charge in units of e
Electron
e, e- , b-
-1
Proton
p
+1
Neutron
n
0
Anti-electron (positron)
b-
+1
Anti-proton
p
-1
Anti-neutron
n
0
Alpha particle
a or 4He++
+2
Up quark
u
+2/3
Down quark
d
-1/3
Any element of atomic
number, z
Z
z
NX
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How Charges Behave in materials
Conductors– charges move freely
 Insulators—charges cannot move easily
 Semiconductors—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
U  Th  He
238
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X
4
2
What is X?
e  b  Energy


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Coulomb’s Law
Charles Augustin de Coulomb used a torsion pendulum to establish
“Coulomb’s Law”

q1q2
F  k 2 rˆ
r
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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


p =3.1415928….
e0 = 8.854 x 10-12 C2/(N·m2)

Called the permittivity of free space
k
1
4pe0
 9 109
N  m2
C2
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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.
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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 a
sphere with a
hole in it
The E-field of the
whole sphere
=
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 diagram


Show 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?
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
Have I seen this before?
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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?
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
1.
2.
3.
Rules for Field Lines
Electric field lines point
to negative charges
Electric field lines
extend away from
positive charges
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

q
E  k 2 rˆ
r
This quantity represents an infinite set of
vector quantities, in other words, a vector
field.
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The Problem

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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

dq
dE  k 2 rˆ
r
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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
dq

q

and

q
E  k 2 rˆ
r
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4 Geometrical Situations-Line Charge


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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, l (units C/m)
ds  dx or dy or dz
dq
l
ds
dq  lds
and
dE  k
lds
r2
ds  drd
ds  2pdr
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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, s (units
C/m2)
dq
s
da
dq  s da
and
dE  k
da  rdrd 
da  2prdr
da  dxdy or
s da
r2
dydz or
dxdz
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4 Geometrical Situations-Volume Charge

Volume charge: All
charge resides in a
particular volume
 volume charge
density, r (units
C/m3)
dq
r
dV
dq  r dV
and
dE  k
dV  dxdydz
r dV
r2
dV  r 2 dr sin  d d
dV  4p r 2 dr
dV  rdr d dz  2prdr dz
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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 molecules

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Positive 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?


Recall: t=r x F
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If F=qE, then t=qE r sin ( where  is the angle between E
and r)
Let d=distance between two charges
Electric Dipole Moment
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Principle of microwave oven, amongst other applications
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
t=pE sin or t=p x E
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Potential Energy
Recall that DW=-DU
 DW=F·r=Fr cos=qEd cos
 DU=-qd E cos
 U = - p·E which is the potential energy of
a dipole in an electric field
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