Transcript Electrostatics Power Point

Electrostatics
10.1 Properties of Electric Charges
Static electricity – not moving
Two types of charge
positive (+) when electrons are lost
negative (-) when electrons are gained
Objects can gain charges by rubbing
10.1 Properties of Electric Charges
Like charges repel
Unlike charges attract
Law of Conservation of electric charge – the
net amount of electric charge produced in a
process is zero
10.1 Properties of Electric Charges
Robert Millikan – charge is always
a multiple of a fundamental unit
Quantized – occurs in discrete
bundles
The discrete bundle is an electron
The charge on a single
electron is
1.602 x10
19
C
10.1 Properties of Electric Charges
10.2 Insulators and Conductors
Conductors – outer
electrons of atoms
are free to move
through the
material
Insulator – electrons
tightly held, do
not move
10.2 Insulators and Conductors
Semiconductors – conduct electricity under
some circumstances, don’t under other
conditions
Charges can be transferred by contact
Called Charging by Conduction
10.2 Insulators and Conductors
Induction – charging without
contact
Object is brought near a
charged object
Electrons move
Object is grounded
An electroscope measures if
an object has a charge on
it
10.2 Insulators and Conductors
10.3 Coulomb’s Law
Electric charges apply forces to each other
From experiments
Force is proportional
to charge
Inversely proportional
to square of distance
q1q2
F k 2
r
k  8.988 x10 Nm / C
10.3 Coulomb’s Law
9
2
2
Equation – gives magnitude of force
Opposite charges – force directed toward
each other
Like charges – force directed away from each
other
Charge is measured in Coulombs
10.3 Coulomb’s Law
1 Coulomb is the amount of charge, that if
placed 1 m apart would result in a force of
9x109 N
Charges are quantized – that is they come in
discrete values
e  1.602 x10
19
C
The constant k relates to the constant called
the permittivity of free space
 0  8.85 x10 C / Nm
12
2
10.3 Coulomb’s Law
2
These are forces, so be sure to use vector
math, draw free body diagrams
For multiple objects, require multiple free body
diagram
10.3 Coulomb’s Law
10.4 The Electric Field
Electrical forces act over distances
Field forces, like gravity
Michael Faraday
electric field – extends
outward from every charge
and permeates all of space
The field is defined by the force
it applies to a test charge
placed in the field
10.4 The Electric Field
The Electric field would then be
F
Or
E
kq
E 2
r
q
q is the test charge
We can also say that F  Eq
Remember that E is independent of the test
charge.
The electric field is also a vector (free body
diagrams are probably a good idea)
10.4 The Electric Field
10.5 Electric Field Lines
To visualize electric fields
Draw electric field lines
Direction of the lines is the
direction of force on a
positive test charge
The density of the lines
indicates relative
strength of the field
Note: the field density increase
as you get closer
10.5 Electric Field Lines
For multiple charges, keep in mind
1. Field lines indicate the direction of the field
The actual field is tangent to the field lines
2. The magnitude of the field is relative to the
field line density
3. Fields start at positive and end at
negatives
Field Lines
10.5 Electric Field Lines
If the field is produced by two closely spaced
parallel plates
The field density is constant
So the electric field is
constant
Electric Diple – two
point charges of
equal magnitude
but oppsite sign
10.5 Electric Field Lines
10.6 Conductors in Electrostatic Equilibrium
Electrostatic Equilibrium – when no net motion
of charge occurs within a conductor
1. The electric field is zero
everywhere inside a conductor
2. Any excess charge is on the
surface of a conductor
10.6 Conductors in Electrostatic Equilibrium
3. The electric field just
outside a charged
conductor is
perpendicular to the
conductors surface
4. The charge accumulates
on areas of greatest
curvature
10.6 Conductors in Electrostatic Equilibrium
10.7 Potential Difference and Electric Potential
Electricity can be viewed in terms of energy
The electrostatic force is conservative
because it depends on displacement
Now
PE  W
PE  Fd
PE  qEd
We can calculate this value for a uniform
electric field
10.7 Potential Difference and Electric Potential
Positive test charge – increases when moved
against the field
Negative test charge – increases when moved
with the field
PE
V
q
Electric Potential (Potential) – electric
potential energy per unit charge
10.7 Potential Difference and Electric Potential
Only difference in potential are meaningful
Potential Difference (Electric Potential
Difference) – is measureable
PE
PE
V 
qq
Measured in volts (after
Alessandro Volta)
1J
1V 
1C
10.7 Potential Difference and Electric Potential
If we want a specific potential value at a point,
we must pick a zero point.
That point is usually either
A. The ground
B. At an infinite distance r  
10.7 Potential Difference and Electric Potential
10.8 Electric Potential & Potential Energy
Using calculus it can be shown that the
electric potential a distance r from a single
point charge q is
q
V k
r
Assuming that potential is zero at infinity
Like Potential Difference, this value is a scalar
So
10.8 Electric Potential & Potential Energy
10.9 Potentials and Charged Conductors
1. All points on the surface of a charged
conductor in electrostatic equilibrium are at
the same potential.
2. The electric potential is a constant
everywhere on the surface of a charged
conductor in equilibrium.
3. The electric potential is constant
everywhere inside a conductor and equal
to its value at the surface.
10.9 Potentials and Charged Conductors
10.10 Capacitance
Capacitor – device that stores electric charge
In RAM,
Camera
Flash,
10.10 Capacitance
Simple capacitors consist of
two plate
The symbol for a capacitor
is
The symbol for a cell is
The symbol for a battery is
10.10 Capacitance
When a potential difference is placed across a
capacitor it becomes charged
Charging a Capacitor
This process takes a short amount of time
Time for RC Circuit
The charge on each plate is the same, but
opposite charge
The amount of charge is proportional to the
potential difference
A constant C (Capacitance) gives
Q CV
V
10.10 Capacitance
Capacitance – Unit Farad
1C
1F 
1V
For a parallel plate capacitor, the capacitance
depends on the area of the plates, the
distance between the plates
A
C  o
d
10.10 Capacitance
Q  CV
10.11 Combinations of Capacitors
Parallel – more than one pathway
For a parallel set of
capacitors – the total
charge is the sum of
the individual charges
QT  Q1  Q2  ..Qn
In all parallel circuits – the potential across
each branch is the same as the total
VT  V1  V2  ..Vn
10.11 Combinations of Capacitors
The equivalent capacitance is the value of one
capacitor that could replace all those in the
circuit with no change in charge or potential
Since
Q  Q  Q  ..Q
T
And
We combine and get
1
2
Q  CV
CeqVC

C1C
V1  C2V2 ..C..nCnVn
T eq
10.11 Combinations of Capacitors
n
Series – components of a circuit are in one
pathway
The magnitude of the charges is the same on
each plate Q  Q  Q  ..Q
T
1
2
n
10.11 Combinations of Capacitors
The total potential is the sum of the potential
drops across each capacitor
VT  V1  V2  ..Vn
We then use that equation and the equation
for capacitance
Q
V
We get
C
Q1n
Q1T Q
11 Q12
 
 ..
Ceq C1 C2
Cn
10.11 Combinations of Capacitors
10.12 Energy Stored in a Charged Capacitor
Capacitors store energy
Energy can be defined as change in work
W  QV
Or the are under a plot of Q vs. V
UW QQVV
11
22
U  CV
1
2
2
2
Q
U
2C
10.12 Energy Stored in a Charged Capacitor
10.13 Capacitors with Dielectrics
Most capacitors have an insulator between
the plates
Called a Dielectric
Increases the
capacitance by
a factor K
Called the dielectric
constant
o
A
C  K
d
10.13 Capacitors with Dielectrics
Some Dielectric Constants
Material
K
Paper
3.7
Glass
5
Rubber
6.7
Mica
7
Strontium
Titanate
300
10.13 Capacitors with Dielectrics