do now (11/11/13): what do you know about electric charges? what do you think the word...
TRANSCRIPT
Do Now (11/11/13):
What do you know about electric charges? What do you think the word “electrostatics”
means?
Pass your HW in please!
Electrostatics
Bad Hair Day
Static Charges
Rub a balloon on a wool sweater and it will stick to the wall. Why?
Rubbing a balloon on a wool sweater creates charges on the surfaces. Electrons are added or subtracted from the atoms.
Charges That Things Accumulate
• Very positive• Human hands (usually too moist,
though)• Rabbit Fur • Glass • Human hair • Nylon • Wool • Fur • Lead • Silk • Aluminum • Paper • Cotton • Steel
• Neutral
•Neutral• Steel • Wood • Amber • Hard rubber • Nickel, Copper • Brass, Silver • Gold, Platinum • Polyester • Styrene (Styrofoam) • Saran Wrap • Polyurethane • Polyethylene (like Scotch Tape) • Polypropylene • Vinyl (PVC) • Silicon • Teflon
• Very negative
Charging an Object by Touching
++
+++ Two Objects—one
is charged
Objects touch—charge is transferred
+++ +
+
+++ +
+
Objects separate—both are charged
Behavior of Electric Charges
Charging an Electroscope
An electroscope is a device that permits us to explore the concepts of induction and conduction charging.
Charging by Contact
Some electrons leave rod and spread over sphere.
Charging by Induction
Rod does not touch sphere. It pushes electrons out of the back side of thesphere and down the wire to ground. The ground wire is disconnected toprevent the return of the electrons from ground, then the rod is removed.
Charge Distributions
Charge on Metals Charge on Insulators Charge on Metal Points
Excess charge on the surface of a metal of uniform curvature spreads out.
Charge on insulating materials doesn't move easily.
Excess charge on a metalaccumulates at points.
Lightning, lightning rods.
Charges on a Conductor
Attracting Uncharged Metallic Objects
Electrons are free to move in metals.
Nuclei remain in place; electrons move to bottom.
Charges on an Insulator
Attracting Uncharged Nonmetallic Objects
Charges Accumulate on Points
A Shocking Experience
How Lightning Occurs
Electrostatics Is Not Friction
Electrostatic charges are not caused by friction.
The materials involved and the pressure and speed of contact and separation affects the magnitude of the charge. This contact and separation process is known as "triboelectrification," or "tribocharging.“
The suffix tribo means to rub in Greek, thus triboelectrification simply means to electrify (or charge) by rubbing, or by contact.
Applications of Electrostatic Charging
Fine mist of negatively charged goldparticles adhere to positively chargedprotein on fingerprint.
Negatively charged paint adheres to positively charged metal.
Electrostatic Air Cleaner
Electric Forces
The strength of the electric force varies with the square of the distance between the charges
k q1q2
r2
Where k = 8.988 x 109 Nm2/C2 (but approximate 9x109) and a coulomb is the charge which results in a force of
9 x 109 N if placed on two objects 1.0 m apart
F =
Important Numbers
Charge of the electron: -1.6 x 10-19 C = -e Charge of the proton: 1.6 x 10-19 C = +e Mass of the electron: 9.11 x 10-31 kg Mass of the proton: 2000 times electron (1.67 x 10-27kg)
Charges
A coulomb is an extremely large charge Charges produced by rubbing objects are typically
about a microcoulomb The charge of an electron is 1.602 x 10-19 C
Sometimes the force between charges is written as:
F = (1/4πε0) (Q1Q2/r2) where ε0 is the permittivity of free space = 1/4πk =
= 8.85 x 10-12 C2/Nm2
Forces Between Charges
The force field between charges depends on their sign and their magnitude
Electric forces are vectors like all other forces
0.30 m 0.20 m
Q1 = -8.0 μC Q2 = +3.0 μC Q3 = -4.0 μC
Net force on charge 3 will be the sum of F31 and F32
Simple Force Calculation
What is the force between the charges?If the two charges are of opposite sign, what is the direction of the force?
F = k Q1Q2/r2
--------------------------------------k = 9 x 109 N-m2/C2 F = (9 x 109) (5)(8)/22 = 9 x 1010 N
This is an enormous force, because a Coulomb is a huge charge:
One Coulomb is the chargeon 6.25 x 1018 electrons.
Do Now (11/12/13): Three Charges on a Line
Where may any test charge q be placed between the charges if it is to experience zero electric force?
Three Charges on a Line: Part I
Where may any test charge q be placed between the charges if it is to experience zero electric force?
Force between any two charges: F = kq1q2/r
2
----------------------------------------------------------------
Forces by the two charges must be equal but opposite: Force by red charge = k(5)q / x2 Force by yellow charge = k(8)q / (4-x)2
Forces are equal:
k(5)q / x2 = k(8)q / (4-x)2
Solve for x: x = 1.77 m
Three Charges on a Line: Part II
On the line in which region, A, B, or C, may a point be found at which the net force on a positive test charge q would be zero?
How Lightning Occurs
Electric Force Vectors
Consider the forces exerted on the charge in the top right by the other three:
Electric Fields Produce Forces
The Electric Field Due to a Point Charge
F = kQq0/r2 Define: E = F/q0 = kQ/r2
Electric Fields
An electric field extends outward from every charge and permeates all of space
The electric field is given by the force on a very small test charge q, such that:
E = F/q The field at a distance r from a charge Q is:
E =F/q = kQq = kQ/r2
r2q
Electric Fields
Electric field due to a positive point charge.Arrows point in the direction along which a positive test charge would accelerate.--------------------------------------------------------- F = kQq0/r2 E = F/q0 = kQ/r2
Electric field due to a negative point charge.------------------------------------Arrows point towardnegative charge.Field is sphericallysymmetric.
Field Lines
The field lines indicate the direction of the electric field; the field points in the direction tangent to the field line at any point
The lines are drawn so that the magnitude of the field, E, is proportional to the number of lines crossing a unit area perpendicular to the lines. The closer the lines, the stronger the field
Electric field lines start on positive charges and end on negative charges and the number starting or ending is proportional to the magnitude of the charge
E-Field of Spherical Charge Distributions
E = kQ/r2 = (9x109)(5)/22 = 1.125 x 1010 N/C
Radius of the ball is r = 0.5 m.What is the electric field E2 m from the center of the ball? (Assume uniform distribution)
Electric Field Calculation
E2 = (3.0)2 + (2.0)2
= 13.0
E = 3.61 N/C
= tan-1(2/3) = 33.7 degrees
Symmetry In Electric Field Calculations
Electric Field of Dipoles
Electric Fields Under the Sea
Elephant Gnathonemus detects nearby objects by their effects on the electric field.
Cells in shark detect weak electric fields caused by the operation of the muscles of its prey. Fields as weak as 10-6 N/C are detectable
The Electric Field of a Lightning Strike
The direction of the electric field is from positive to negative despite the fact that the current flow is from negative to positiveThis is consistent with the force on a POSITIVE test charge
Examples of Electric Field Strengths
Source E
(N/C)Source
E (N/C)
House wires 0.01 Thunderstorm 10,000
Near stereo 100 Breakdown of air 3 x 106
Atmosphere 150 Cell membrane 107
Shower 800 Laser 1011
Sunlight 1000 Pulsar 1014
Compare to the field detectable by sharks, 10-6 N/C
Practice:
Complete Problem #10 and #11 in your textbook in Chapter 15
Do Now (11/13/13):
Pick up a green/yellow half sheet from the back of the room on your way in
Review yesterday’s Do Now (the solution is on the back board)
A Parallel Plate Capacitor
= q/A = charge densityE = /0 0 = 8.85 x 10-12 N-m2/C2
0 is called the "permittivity of vacuum"
Example:
A = 0.15 m2
q = 6 x 10-6 C = q/A = 6 x 10-6 C/ 0.15 m2
= 40 x 10-6 C/m2
E = /0
= 40 x 10-6/ 8.85 x 10-12 = 4.52 x 106 N/C
Do Now (11/14/13):
Find a place in the room where you are as far away from as many people as possible.
Write it down. Go stand there.
Electric Field Inside a Conductor
Excess charge inside a metal moves to the surface.
If E weren't zero inside, thefree electrons (not shown)would accelerate.
At equilibrium, all excess charge on a metal resides on the surface of the metal.
Electric Fields and Conductors
In a static situation (charges not moving) the electric field inside a conductor is zero If there were a field, there would be a force on the
free electrons, since F=qE. They would move until they reached positions where the force on them would be zero
Therefore, any net charge on a conductor distributes itself on the surface The charges get as far away from each other as
possible
Electric Fields and Conductors (cont’d)
A charge placed inside a conducting sphere results in charges as shown in the figure
Electric Fields and Conductors (cont’d)
The electric field of static charges is always perpendicular to the surface outside of a conductor If there were a parallel component
of the field, the electrons would move along the surface until they reached positions at which no force was exerted on them.
E-Field is Perpendicular to Conductors in Equilibrium
Uncharged Metal Plate in an Electric Field
Metal plate is polarized by theexternal electric field.
Sheets of charges on plateset up electric field (not shown)which cancels the externalelectric field.
If the electric field E weren't zero inside the metal, what would happen?
What is the field inside a hollow box placed between two charged plates?
If the box was a solid block of conducting material the field inside would be zero
For a hollow box the external field does not change, since the electrons can still move in the same ways
A hollow box is a useful way to protect sensitive electronics from external electric fields, such as produced by lightning
Recognizing Incorrect Electric Field Patterns
This field configuration can't exist because the bottom of the ball will be positively charged, so a field should exist between the plate and the bottom of the ball.
On the left and right sides in this view, the electric field E is tangent to the metal ball, so a tangential force on the electrons would exist, contradicting the fact of equilibrium.
Using Metal to Shield Electronic Components
Electric Flux Through a Plane Surface
Electric Flux = A cos
Electric Flux Through a Closed Surface
Electric Flux = A cos (Some texts use S for the area) ---------------------------------------------------- If there is no net charge inside this closed surface, the net flux is zero: every arrow that enters must exit. E-field vectors which enter a surfaceprovide negative flux, while vectors which exit give positive flux.
Visually we can try to understand that the flux is simply the # of electric field lines passing through any given area.
• When E lines pass outward through a closed surface, the FLUX is positive
• When E lines go into a closed surface, the FLUX is negative
Electric Flux
In the left figure, the flux is zero.
In the right figure, the flux is 2.
Gauss's Law
Friedrich Gauss (1777-1855)
Gauss's Law:
AE cos = q/0 q = net charge inside Gaussian surface This is useful if = 0 and E = constant.
Gauss’ LawWhere does a fluid come from? A spring! The spring is the SOURCE
of the flow. Suppose you enclose the spring with a closed surface such as a sphere. If your water accumulates within the sphere, you can see that the total flow out of the sphere is equal to the rate at which the source is producing water.
In the case of electric fields the source of the field is the CHARGE! So we can now say that the SUM OF THE SOURCES WITHIN A CLOSED SURFACE IS EQUAL TO THE TOTAL FLUX THROUGH THE SURFACE. This has become known as Gauss' Law
Gauss’ Law The electric flux (flow) is in direct proportion to
the charge that is enclosed within some type of surface, which
we call Gaussian.
The vacuum permittivity constant is the constant of
proportionality in this case as the flow can be interrupted
should some type of material come between the flux and the surface area. Gauss’
Law then is derived mathematically using 2
known expressions for flux.
o
encqdAE
Gauss & Michael FaradayFaraday was interested in how charges move when
placed inside of a conductor. He placed a charge inside, but as a
result the charges moved to the outside surface.
Then he choose his Gaussian surface to be
just inside the box.
0
)(0
enc
o
enc
o
enc
q
qA
qdaE
He verified all of this because he DID NOT
get shocked while INSIDE the box. This is called Faraday’s
cage.
Gauss’s Law
For Physics B: E-field inside a conductor is zero
0
)(0cos
enc
o
enc
o
enc
q
qA
qAE
For Closed Surfaces:
Calculus:
Gauss's Law Gives Field Due to a Point Charge
Gauss's Law:
AE cos = q/0
A = area of sphere = 4r2
E is the same at all points on the surface
= 0 cos = 1 (4r2)E = q/0
E = q/(40r
2)
Gauss's Law Application
This is a sheet of charge--not a metalplate. Sheet is very large (edges arenot shown); near center of sheet, the E vector is perpendicular to the sheet.
AE cos = q/0
q = where = charge densityE + A2 (0) + A3E = /0
2AE = /0
E = /0
Gauss’ Law – How does it work?
Step 1 – Is there a source of symmetry?
Consider a POSITIVE POINT CHARGE, Q.
Yes, it is spherical symmetry!You then draw a shape in such a way as to obey the symmetry and
ENCLOSE the charge. In this case, we enclose the charge within a sphere. This surface is called a
GAUSSIAN SURFACE.Step 2 – What do you know about the electric
field at all points on this surface?
It is constant.
o
encqdaE
The “E” is then brought out of the integral.
Gauss’ Law – How does it work?
o
encqrE
)4( 2
Step 4 – Identify the charge enclosed?
The charge enclosed is Q!
Step 3 – Identify the area of the Gaussian surface? In this case, summing each and every dA gives us the surface area of a sphere.
oo r
QE
QrE
22
4)4(
This is the equation for a
POINT CHARGE!
Cylinder with Charge distribution
Charge distribution:
encqLQL
Q
Gauss’ Law and cylindrical symmetryConsider a line( or rod) of charge that is very long (infinite)
+++++
++
+
++
++
We can ENCLOSE it within a CYLINDER. Thus our Gaussian
surface is a cylinder.
o
o
o
enc
o
enc
rE
LrLE
qrLE
qdaE
2
)2(
)2(
This is the same equation we got doing extended charge distributions.
rLA
qLQL
QMacroRECALL
cylinder
enc
2
:
Gauss’ Law for insulating sheets and disksA charge is distributed with a uniform charge density over an infinite
plane INSULATING thin sheet. Determine E outside the sheet.
+
For an insulating sheet the charge resides INSIDE the sheet. Thus there is an electric
field on BOTH sides of the plane.
o
o
oo
o
enc
E
AEA
A
Q
QEA
QEAEA
qdAE
2
2,
2
This is the same equation we got doing
extended charge distributions.
Gauss’ Law for conducting sheets and disksA charge is distributed with a uniform charge density over an infinite
thick conducting sheet. Determine E outside the sheet.
+
For a thick conducting sheet, the charge exists on the surface only
o
o
o
o
enc
E
AEA
A
Q
QEA
qdAE
,
+
+
+
+
+
+
E =0
In summaryWhether you use electric charge distributions or Gauss’ Law you get the
SAME electric field functions for symmetrical situations.
o
enc
oo
qdAE
r
dqdE
r
QE
22 44
Function Point, hoop, or Sphere
(Volume)
Disk or Sheet
(AREA)
“insulating and thin”
Line, rod, or cylinder
(LINEAR)
Equation24 r
QE
o
rE
o
2
o
E
2
Practice:
Complete the multiple choice questions in Chapter 15
Gauss's Law Applied to Parallel Plate Capacitor
Large plates close together; ignore fringing at edges. Electric field inside the metal is zero. E is perpendicular to the plates (far from the edges).
We assume a charge density
E is zero at the left end and E is parallel to the side.
q = A EA = A/0
E = /0
Wimshurst Machine
Invented by James Wimshurst in 1882 The first studies of sparks and
oscillating electrical discharge were made using this type of machine.
Electrostatic machines were fundamental in the early studies of electricity, starting in the XVII century, in the form of "friction machines", and their development culminated at the end of the XIX century with the development of powerful "influence machines".
Theory Of Operation Of A Wimhurst Machine
The disks can be made of plastic, glass, or hard rubber The counter-rotating disks cause air molecules to become electrically
activated by the frictional movement between the disks. This rotating action causes the disks to become continually charged and
an electrostatic charge builds up, which will cause a flash over if not bled off.
To prevent flash over, a series of foil sections are attached to the center portion of each disk and equally spaced and back to back with foil sections on the outer sides.
To remove the charge, collection arms are arranged to collect the charge and transfer the charge to a storage capacitor.
At 45 degrees to these collection points is a neutralizing bar that extends the full length of the disk and has brushes at both ends.
A neutralizing brush equals the charges on the metal foil position at both positions on both sides. The neutralizing bar on opposite side disk is at ninety degrees to the one for the other side.
Van de Graaff Generator
Van de Graaff Generator
How It Works
When the motor is turned on, the lower roller (charger) begins turning the belt.
Belt is made of rubber and the lower roller is covered in silicon tape, Lower roller begins to build a negative charge and the
belt builds a positive charge. Silicon is more negative than rubber; therefore, the lower
roller is capturing electrons from the belt as it passes over the roller
Positive charges from belt are deposited on sphere
Cereal Storm
Van de Graaff Generator
A. Output terminal—an aluminum or steel sphere
B. Upper Brush—A piece of fine metal wire
C. Upper Roller—A piece of nylonD. Belt--A piece of tubingE. Power supplyF. Lower BrushG. Lower roller—nylon covered with
silicon tape
Do Now (11/18/13):
Define the following in your own words. If you do not know, hypothesize:
Capacitance Voltage Potential
Definitions
Electric Field = force per unit charge Electric Potential = potential energy per unit charge
electric potential = electric potential energy charge
Vab = Va – Vb = -Wab/q
The change in electric potential is the work done on a unit charge
1 volt = 1 joule/coulomb
Brainstorm:
The charges that flow through the wires in your home ____.
a. are stored in the outlets at your home
b. are created when an appliance is turned on
c. originate at the power (energy) company
d. originate in the wires between your home and the power company
e. already exist in the wires at your home
Voltage Sources
To do useful work voltage sources capable of maintaining a steady current flow are required Generators Batteries Fuel cells
Voltage provides the force to “push” electrons through a circuit
Electric Potential
Just as with gravitational potential energy, the zero point of electric potential is an arbitrary location
The larger rock has the greater potential energy; the larger charge has the greater electric potential energy
Relationship Between Electric Potential and Electric Field
The effects of a charge distribution can be described using either the electric field or the electric potential Electric potential is a scalar which makes it sometimes easier to
use Work done by the electric field to move a positive charge
q from b to a is:W = qVba
If there is a uniform field between two plates, the work can be written as:
W = Fd = qEd Therefore, Vba = Ed or E = Vba/d The units of electric field are either V/m or N/C,
1 N/C = 1 V/m
Example
Two parallel plates are charged to 50 V. If the separation between the plates is 0.050 m, calculate the electric field between them
E = V/d = 50 V/ 0.050 m
= 1000 V/m
Equipotential Lines and Surfaces
Along equipotential lines and surfaces, all points are at the same potential An equipotential
surface must be perpendicular to the electric field at any point
Equipotential Examples #1
The potential along an equipotential curve is the same at any point
Equipotential lines are perpendicular to the electric field lines
Equipotential Examples #2
As we move a charge from one equipotential line to another we change its electric potential
It takes the same amount of work to pull a charge to one spot on the curve as it
does to pull it out to a different spot on the curve. That means that the work
done per unit of charge (electric potential) is also the same.
The work done was 10J on 1C so the potential difference is 10J/C or 10
volts.
V = W/qmoved
Electron Volts
A joule is a large unit of measure when charges of the size of electrons are considered
An electron volt (eV) is defined as the energy acquired by a particle carrying a charge equal to that of an electron when it is moved through a potential difference of one volt
1 eV = 1.6 x 10-19 J
Electric Potential of a Point Charge
The electric potential at a distance r from a point charge Q is given by:
V = (1/4πε0) (Q/r)
= k (Q/r)
V goes to zero as r → ∞
Work to Force Two + Charges Together
What is the minimum work required to move a
charge q = 3.0 μC from a great distance (r = ∞) to a point 0.5 m from a charge Q = 20.0 μC?
The work required is the change in potential energy:
W = qVab = q (kQ/rb – kQ/ra)
= (3 x 10-6 C) (9 x 109 Nm2) (2.0 x 10-5 C) = 1.08J
(0.5m)
Which Has the Most Potential Energy?
Positive energy
Largest negative energyHardest to separate
Capacitors
A capacitor is a device for storing electric charge The simplest capacitor consists of two parallel
conducting surfaces If a voltage is applied to a capacitor it
becomes charged The amount of charge is given by Q = CV where
C is called the capacitance of the capacitor Capacitance is measured as coulombs per volt
and this unit is called a farad
Capacitance
The capacitance C is constant for a given capacitor It does not depend on Q or V; it
depends only on the structure of the capacitor
For parallel plates of area A separated by a distance d in air the capacitance is given by:
C = ε0A/d
Dielectrics
In most capacitors the conducting layers are separated by an insulating material that is called a dielectric
The dielectric increases the voltage that can be applied to the plates before they short out and they can be placed closer together
The dielectric increases the capacitance of the capacitor by a factor K which is called the dielectric constant
C = Kε0A/d or C = εA/d where ε = Kε0
How a Dielectric Works
Consider a capacitor with charges +Q and –Q on its plates The voltage between
the plates is Q = CAVA where the subscript A refers to having air between the plates
How a Dielectric Works #2
Now place a dielectric between the plates The electric field between
the plates will induce charges in the dielectric even though the charges can’t flow
The net effect is as if there were a net charges on the outer surfaces of the dielectric
The force on a test charge q within the dielectric is reduced by the factor K because some of the field lines no longer go through the dielectric
How a Dielectric Works #3
Because the field is reduced within the dielectric the force on the test charge is reduced by a factor of K The voltage is now given by V = VA/K
But the charge on the plates has not changed so Q = CV where C is the capacitance with the dielectric present
We can write: C = Q/V = Q/(VA/K) = QK/VA = KCA
Therefore the capacitance is increased by the factor K
Common Dielectric Constants
Example
A capacitor consists of two plates of area A separated by a distance d connected to a battery of voltage V from which it acquires a charge Q
Since the capacitor remains connected to the battery, the voltage V must remain the same
But inserting a dielectric increases the capacitance C and Q = CV
Therefore, if C increases, Q must also
While connected to the battery a dielectric is inserted
Will Q increase, decrease, or stay the same?
Storage of Electric Energy
A charged capacitor stores electric energy The energy in a capacitor is equal to the work done to
charge it The net effect of charging a capacitor is to move
a charge from one plate to another As more and more charge accumulate on a plate, the
harder it becomes to put more charge on it The energy in a capacitor is
U = ½QV = ½CV2 = ½Q2/C since Q = CV
Example
A camera flash unit stores energy in a 150 μF capacitor at 200 V How much electric energy is stored?
U = ½CV2 = ½(150 x 10-6 F)(200 V)2
= 3.0 J Notice that
FV2 = (C/V)(V2) = CV = C(J/C) = J
Cathode Ray Tubes (CRTs)
In a cathode ray tube, electrons are boiled off a hot electrode and are accelerated by a potential of 5-50 kV The electrons are steered onto the screen by pairs of parallel
deflection plates Changing the voltage on the deflection plates will change the
position of the electrons on the screen
Do Now (11/19/13):
Draw a parallel circuit Draw a series circuit What is the difference between the two?
Multiple Capacitors
When used in circuits capacitors can be either in series or parallel
When connected in parallel, the voltage is the same across all capacitors
Q = Q1 + Q2 + Q3 = C1V + C2V + C3V A single capacitor with the equivalent
capacitance can be written as Ceq
Therefore,
CeqV = C1V + C2V + C3V or
= C1 + C2 + C3
Capacitors in series just add The effect is as if the surface area of the
plates was increased
How Lightning Occurs
When Charges Move Against Forces, Work Is Done
• In order to bring two like charges near each other work must be done. In order to separate two opposite charges, work must be done.
• As the monkey does work on the positive charge, he increases the energy of that charge. The closer he brings it, the more electrical potential energy it has. When he releases the charge, work gets done on the charge which changes its energy from electrical potential energy to kinetic energy.
Practice:
Complete the multiple choice questions in Ch. 16