11 sept (where are we?)
• Q  F  E
• Charge gives force which can be
described by field
• Recall mechanics last year….
– Force can be analyzed, chapter 5
– Chapter 6: what value is energy to physics?
• ________________________________
– Same value to electrical forces! Same
language!
– But “potential energy” is a difficult concept.
14 sept: Review chapter 6
• W = FII d
• Define PE as “energy dependent on position”
– With respect to any forces being applied
– PEg = mgh when the force is mg
– PEs = ½ k x2 where avg force is ½ kx
• KE = ½ mv2
• TOTAL E is always conserved, includes NC
• Mechanical energy is conserved only
IF NO DISSIPATION BY NC FORCES
• Check: solve a falling ball using energy concepts
(open book, use chapter 6)
Chapter 17
Electric Potential
Units of Chapter 17
• Electric Potential Energy and Potential
Difference
•Relation between Electric Potential and
Electric Field
•Equipotential Lines
•The Electron Volt, a Unit of Energy
•Electric Potential Due to Point Charges
•Potential Due to Electric Dipole; Dipole
Moment
Units of Chapter 17
• Capacitance
• Dielectrics
• Storage of Electric Energy
• Cathode Ray Tube: TV and Computer
Monitors, Oscilloscope
• The Electrocardiogram (ECG or EKG)
17.1 Electrostatic Potential Energy and
Potential Difference
News: The electrostatic force is
conservative –thus, potential
energy can be defined
Change in electric potential
energy is negative of work done
by electric force:
Is Simple for uniform field
Note: F = qE is constant along the
field only if E is constant.
Turn this sideways for analogy to gravity…
And we remember …. PEb – PEa = -mgd
Check: why is this negative?
b is lower than a
So there is electrical potential
energy.
17.1 Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as potential
energy per unit charge:
(17-2a)
Unit of electric potential: the volt (V).
1 V = 1 J/C.
It takes one J to move one C through 1V
It takes energy to move charge through
a voltage difference
*17.1 Electrostatic Potential Energy
and Potential Difference
Note: Only changes in potential can be
measured, allowing us to pick where V = 0.
Also, we know we can relate DPE to work.
(17-2b)
17.1 Electrostatic Potential Energy and
Potential Difference
Analogy between gravitational and electrical
potential energy:
Does size matter to the potential energy?
17.2 Relation between Electric Potential
and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by
distance:
Assuming E
is constant or
uniform!!
17.2 Relation between Electric Potential
and Electric Field
So, for the uniform field,
Uniform
field
If the field is not uniform, it can be
calculated at multiple points:
Or as -dV/dx
Check: I have a field of 10 V/m. What is
Voltage diffence over 0.25m?
Units of E
• N/C
• V/m
• So what is a volt?
Charges “falling”
• A positive charge will fall from high PE to
low PE
– from high V to low V
• A negative charge will fall from high PE to
low PE
– From low V to high V
Each contour line is 5 feet ver
Each contour line is 20 feet vertical
The topographical map
• An equipotential graph for PEg
• Look at a few
• How much work to walk along a contour
line (iso-elevation)?
• Check: walk from low elevation to high
elevation, how much work?
• In electric potential field, move a + charge
from low V to high V, how much work?
17.3 Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
17.3 Equipotential Lines
What is the most direct path from low to
high potential?
The E field line!
Drawing equipotential lines
• Perpendicular to the e field lines
• Can’t cross each other
• Draw close in first:
– Circular on pt charge
– Line parallel to charged plate
• Draw the far away view:
• Don’t worry about spacing of equipotential lines
unless specifically asked for this.
• E field lines and isopotential lines are
perpendicular
*Practice drawing equipotential
lines
1. Negative point charge
2. Pos and negative point charge
See examples here:
http://vnatsci.ltu.edu/s_schneider/physlets/m
ain/equipotentials.shtml
3. And try to draw the side view of simple
cases
17.4 The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
We won’t use this much, but it’s a useful
unit for very small energies, ie. In chemistry.
Viewing and solving point charge problems
• P- for example
• http://vnatsci.ltu.edu/s_schneider/physlets/main/equipotentials.shtml
for viewing (use Internet Explorer if Chrome fails)
• look at unequal-unlike charges
• Sketch side view (elevation)
+
V=0
-
Using equipotential lines
The lines mean something
quantitative and physical about
moving charges.
How much work to move a 0.2C
charge to the middle of this circle
from far away?
1v
2v
6v
4v
3v 2v 1v
12v
+
How fast will
the particle of
.001 C and
mass 1 mg be
going at 1V?
Look at HW P-1,3,5,7,11
equations so far
KE = ½ m v2
Wadded + WNC = DKE + DPEg + DPEs
Sept 16: 17.5 Electric Potential Due to
Point Charges
The electric potential due to a point charge
can be derived using calculus, which we
won’t do.
(17-5)
recall….what = kQ/r2
???
17.5 Electric Potential Due to Point
Charges
These plots show the
potential due to (a)
positive and (b) negative
charge.
Note how the shape of the E and V differ as
we leave a point charge……
1.2
1
0.8
0.6
E
V
0.4
0.2
0
0
2
4
6
distance
8
10
12
18 sept: 17.5 Electric Potential Due to
Point Charges
Using potentials instead of fields can make
solving problems much easier – potential is a
scalar quantity, whereas the field is a vector.
Do example 17-5, and note that
charges are brought in
from r = infinitely far away.
Quiz 17 Sep
• I place this charged globe at -4.00nC on a
table.
– What is E due to this ball 30.0cm away?
– What is F on an electron that is 30.0cm away?
Amazing analogy of physics
between gravity and electricity
Gravity
units
Electricity
units
fundamental quantity
m
kg
q
C
force between two bodies
GmM/r2
N
kqQ/r2
N
field due to body
g = GM/r2
N/kg or
m/s2
E = kQ/r2
N/C
force in field of body
mg
N
qE
N
potential
gh = GM/r
N m/kg
V = kQ/r
N m/C
Potential energy
mgh = GmM/r
J
qV = kqQ/r
J
Displacement in field to give
potential
h = Dr
m
Dr
m
Universal constant
G
N m2/kg2
k
N m2/C2
Gauss’s Law
We need it, so let’s go back into
16 and cover it.
Coming back to-16.10 Gauss’s
Law Electric flux:
(16-7)
Electric flux, plus or minus,
through an area is
proportional to the total
number of field lines
crossing the area.
16.10 Gauss’s Law
Flux through a closed surface:
16.10 Gauss’s Law
The net number of field lines through the
surface is proportional to the charge
enclosed, and also to the flux, giving
Gauss’s law:
(16-9)
This can be used to find the electric field
in all situations, and we can actually
solve without computers for cases with a
high degree of symmetry.
*So now use Gauss’s Law
• Field around a point charge
• Is E constant at given r? Then pull it out of
sum.
• What is sum of all DA over a sphere of
radius r?
• Simplify and find Coulombs…..
17.6 Potential Due to Electric Dipole;
Dipole Moment
A special case that we won’t worry about:
The potential due to an electric dipole is
just the sum of the potentials due to each
charge, and can be calculated exactly.
17.6 Potential Due to Electric Dipole;
Dipole Moment
Approximation for potential far from
dipole:
(17-6a)
17.6 Potential Due to Electric Dipole;
Dipole Moment
Or, defining the dipole moment p = Ql,
(17-6b)
Jamie Harris, 23,
was struck by
lightning on Aug.
15, 2012 while at
Brainerd. He
doesn’t
remember
anything from the
event, but has
burns on his
arms and singe
marks and two
holes in the Tshirt he was
wearing.
Lightning: how it works
HSvideo: http://www.youtube.com/watch?v=JVXy-ZqqZ-g
Discovery(5min) http://www.youtube.com/watch?v=Q3Awp3CxSU&feature=related
http://petapixel.com/2012/07/24/jaw-dropping-slow-motion-footage-of-lightningshot-at-7207-fps/
http://what-if.xkcd.com/16/ is a little Q&A about lightning (check here for the fast
video he mentions http://vimeo.com/28457062) You are becoming experts on
lightning, so here's some interesting facts.
• Charge separation in the cloud, probably
induction (as in the Wimshurst generator).
•
Physics Look at the bottom diagram to see field lines:
http://regentsprep.org/Regents/physics/phys03/alightnin/default.htm
Lightning
• http://io9.com/new-statistics-on-lightningdeaths-in-the-u-s-reveal-w-560760736
• Know this about lightning
–
–
–
–
–
–
–
Charge separation, cloud as a capacitor
Induction on the ground
Field line concentration on ground
Charge separation in air
Leader pours out of cloud, goes to ground
Streamer comes up from ground to meet leader
Discharge, flash, and boom
Fields around the Van de Graaff
•
•
•
•
How does this machine work?
Sketch the field around the head.
Sketch the potential lines around the head.
Now add a pin or sharp edge and redraw.
Quiz 24 sept
• I have a point charge in isolation of charge
-q.
– What is the field strength and direction a
distance r from the charge?
• Using Gauss’s Law, derive a relation for E
as a function of r from a charge –q.
Quiz 24 sept
• The VandeGraaf generator has a charge
of -1.0 mC.
• The globe has a charge as measured and
shown.
• They are separated by 3.0 m
• 1. What is the force between them?
• 2. What is V and E at the position midpoint
between them?
*21 Sept: 17.7 Capacitance
A capacitor consists of two conductors
that are close but not touching. A
capacitor has the ability to store electric
charge.
Storage of charge
• Means “long-term” holding of net positive
or negative charge in a particular place.
• It is a static situation – the charges are not
moving
• Check: what storage of charge have we
seen in the classroom so far?
How can such storage be useful?
• It can be slowly charged and immediately
released?
• I will take a photo of the person who gives
a common example?
• Capacitor: a place to hold separated
charges in a stable manner.
• A very important circuit element
– Show examples in circuit boards
17.7 Capacitance
Parallel-plate capacitor connected to battery. (b)
is a circuit diagram.
Our first circuit!
17.7 Capacitance
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
(17-7)
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
Review of fields and
equipotentials
• http://ephysics.physics.ucla.edu/physlets/1
.1/e_electric_field.htm
• I give you a charge landscape, you draw
the elevation picture
• Review electron V and PE in a field E.
Example question 1
•
a.
b.
c.
d.
(3pts) A negative charge is moved from point A to point B along an electrical
field line. Which is correct?
The negative charge performs work in moving from point A to point B.
Work is required to move the negative charge from point A to point B.
Work is both required and performed in moving the negative charge from
point A to point B.
No work is required to move the negative charge from point A to point B.
+
a
b
E
Example questions 2&3
2. A field E in our lab points up, and a dust
particle mass m and charge +q is
suspended in equilibrium.
– Write an equation relating E, m, and q.
3. What is the change of potential if I move
from 1.0 m to 2.0 m away from a 1.0 C
charge?
A practice problem like the quiz
• An electron is 2.0m from a proton. (use qe
as variable for electron or proton charge)
a. What is the potential at the position of the e-?
b. I move the e- to a position 8.0m from the
proton. What is the new potential at that
position?
c. What is DPE for this action in part b?
d. If I now release the electron, what will it’s
speed be when it returns to its original
position?
21 sept: 17.7 Capacitance
The capacitance does not depend on the
voltage; it is a function of the geometry and
materials of the capacitor.
For a parallel-plate capacitor:
(17-8)
Check: how much charge in this1 F capacitor
loaded with 5V?
Assume plate separation is 0.03mm. What is A?...
mm
.03
F
N m2
C
VC
m
1.0
1000
8.85x10-12
C2
FV
Eqn 17-7
Nm
mm
Eqn 17-2a
Area = 3.4x106 m2 !!!!!!!!!!!!!!!!!!!!!!!!
For the 1F capacitor of 4cm diameter
and 1 cm height.
28 sept: A check problem
• Show + point charge in middle of page
– Draw 8 field lines
– Draw 4 equipotential lines of equal difference
• Remember that V = kQ/r
– Draw elevation (side view) of potential
V
0
Distance from charge
Key points about capacitors
• Once the charge is loaded, Q will remain
constant unless it is added or removed
with a conductor.
• Q=CV always
• C = eo k A/d
*17.8 Dielectrics
A dielectric is an insulator, and is
characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled
with dielectric:
(17-9)
Note: be very careful….
capacitance is C and Coulomb unit is C !!!...........
**17.8 Dielectrics
Dielectric strength is the
maximum field a
dielectric can experience
without breaking down.
You don’t have to memorize
these, but be able to
use them.
practice: how much charge can I store
on a 0.10 m2 capacitor with
0.1mm separation and mica dielectric?
17.8 Dielectrics
The molecules in a dielectric tend to become
oriented in a way that allows more electrons to
be packed on with less “pressure”.
A quiz on chapter 17
Please turn this in.
• Analogies: fill in the missing cells below
Name
Gravity
Electrical
A. Fundamental
quantity
B. Field
g = GMearth/Rearth2
C. Potential
energy
D. Potential
gh = GM/R
• Given the charges drawn on the board
– Sketch the field lines
– Sketch the isopotential lines
– Sketch the plot of V vs. x
– Identify any locations where E or V is zero
Quiz on 16 and 17
• A negative point charge of –q and mass
10M is fixed in space. A second charge of
4q and mass M is located a distance L
away.
a. What is potential at position of 4q?
b. What is PE between the charges?
c. If I release –q, what will be its initial
acceleration? (magnitude and direction)
d. What will be the final a of the –q charge?
e. What will be the final v of the –q charge?
Practice 27 sept
• Start with charges arranged as below.
a. What is potential at each corner due to
other charges?
b. If charge +Q, mass m is released, what
will it’s velocity be after a long, long time?
2Q
Q
-Q
F=kqQ/r2
Q= CV
V = kq/r
V = -Ed
PE = qV
KE = ½ m v2
Practice the vectors
• (10 points) Three charges are separated as shown below with
charges shown. Draw the individual force vectors on each charge
(using dashed lines), and the resultant force vector on each
charge (using solid lines). Draw very carefully so the relative
magnitudes of each force are accurately depicted. No calculation
is necessary.
-2Q
-4Q
+2Q
Return exam 1
•
•
•
•
•
Lab on static loss with air flow: 18 pts
Lab on Coulomb force on pith: 30 pts
Exam: 112 pts possible
Total all three,
Average =
, high 100%
17.9 Storage of Electric Energy
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
The capacitor is like a spring, and the spring
gives back the energy you put in. PE = ½ k x2
(17-10)
PE is also labeled as U
KE is also labeled as K
17.9 Storage of Electric Energy
The energy density, defined as the energy per
unit volume, is sometimes a useful number to
use. Works for any field, any place, vacuum or
solid.
(17-11)
Note that e0 appears again:
k = 1/4pe0
C = e0 A/d
And energy and energy density
Electrical charge and animal health
Why, or how, can electricity jump
start the heart?
How can electrical probes (EKG) tell
us about the heart beating?
Heart defibrillators use electric
discharge to “jump-start” the
heart, and can save lives.
What good is a capacitor?
• Stores charge. So what?
• Stores energy U
1. Stores slowly and released quickly
2. Stores quickly that can be released
slowly
3. Store and hold for long time w/o battery
4. Stores and releases with very specific
time (as we will learn)
4 Oct: Capacitors connected
C1 = e0A1/d1
C2
• Connect in parallel
– Ctotal = C1 + C2 : think of adding area
– Qtotal = Q1 + Q2: charge is conserved
– So Vcombined = Qtotal/Ctotal
– problem 41 example
Solving capacitor problems
• Identify what is constant…
– Usually Q is constant
• Identify what is changing….
– Usually V and C are changing
• Solve the initial condition
• Use equations to solve final condition
The amazing analogy of physics
between gravity and electricity
Gravity
units
Electricity
units
fundamental quantity
m
kg
q
C
force between two bodies
GmM/r2
N
kqQ/r2
N
field due to body
g = GM/r2
N/kg or
m/s2
E = kQ/r2
N/C
force in field of body
mg
N
qE
N
potential
gh = GM/r
m2/s2
V = kQ/r
N m/C
Potential energy
mgh =
GmM/r
h = Dr
J
qV = kqQ/r
J
m
Dr
m
Displacement in field to give
potential
Universal constant
G
N m2/kg2
k
N m2/C2
1 oct: 17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
A cathode ray tube
contains a wire cathode
that, when heated, emits
electrons. A voltage
source causes the
electrons to travel to the
anode.
+
What is
this?
anode
Control
grid
cathode
heater
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
The electrons can be steered using electric or
magnetic fields.
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
Televisions and computer monitors (except for
LCD and plasma models) have a large
cathode ray tube
as their display.
Variations in the
field steer the
electrons on their
way to the screen.
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
An oscilloscope displays en electrical signal on
a screen, using it to deflect the beam vertically
while it sweeps horizontally.
Capacitor lab
• Need to transfer charge to the capacitor.
– can use fixed V
– Can use fixed Q
• Calibrate the transfer wand using 3000V globe and
faraday cage; find Q/aliquot
• show set up
• Train electrometer safety
• Hand out lab assignment “analyzing
simple parallel plate capacitor”
• Leyden jar for extra credit (google it)
Quiz 22 sept
• I put the charged rod in the faraday cage
and show the measured charge with
loggerpro. It is -57nC.
– What is E at 3.0 m
– What is V at 3.0 m
– What is the rate of electron- loss given slope
shown of .003521 nC/s?
– Allow 1 or 2 sf.
17.11 The Electrocardiogram (ECG or EKG)
The electrocardiogram
detects heart defects by
measuring changes in
potential on the surface
of the heart.
Summary of Chapter 17
• Electric potential energy:
• Electric potential difference: work done to
move charge from one point to another
• Relationship between potential difference
and field:
Summary of Chapter 17
• Equipotential: line or surface along which
potential is the same
• Electric potential of a point charge:
• Electric dipole potential:
28 sept: Summary of Chapter 17
• Capacitor: nontouching conductors carrying
equal and opposite charge
•Capacitance:
• Capacitance of a parallel-plate capacitor:
And with K
Summary of Chapter 17
• A dielectric is an insulator
• Dielectric constant gives ratio of total field to
external field
• Energy density in electric field:
The equations of importance, chapter 17.
F = k Q1Q2/r2
E = F/q
W = F . d = DPE for conservative force
V = W/q = E . d
V = kQ/r
DPE = qV
•For parallel plate capacitor
Q=CV
U = ½ Q2/C = ½ QV
C = ke0A/D
F = k Q1Q2/r2
This is how they’ll be
E = F/q
given on the exam,
V = W/q
meaning you have to sort
V = kQ/r
them out. Which are point
DPE = qV
charge, and which pp, and
Q=CV
which for any?
C = ke0A/D
U = ½ Q2/C = ½ QV
R = r L/A
rT = ro[1 + a (T-To)]
e0 = 1/(4pk) = 8.85x10-12 C2/N.m2
k = 1/(4pe0) = 9.0 x 109 N.m2/ C2
r for copper = 1.68 x 10-8 W m
P = IV
UNITS get confusing.. so be careful
The Quantity…
• Charge, q, Q
• Field E
• potential V
• potential energy PE or U
• capacitance C
•
•
Is in Units of…
• Coulombs, C
• N/C [=] V/m
• Volt V [=] J/C
• J [=] V C
• Farads F [=] C/V
•
•
Know the equations, and work out the units
from them….
Demo with pp capacitor
• Show 3000v loading and discharge
– What happens to plates as discharge
happens?
• Load 30v on plate, and move apart
– What happens to voltage?
– Is it consistent with theory?
– Why would potential go up?
– How much charge stored at 30V? At 3000V?
Lab 1, capacitor fundamentals
• Introduce and hand out sheet
• Assign groups
• Schedule
Capacitors connected
• P 66 has them in series.
• How to solve?
• Think about charge!
Practice field lines and potential lines and elevation plots
•
Use http://vnatsci.ltu.edu/s_schneider/physlets/main/equipotentials.shtml
Writing stronger analysis
sections in your labs
• Hand out: “analysis portions by Dr. R.
Fisher, ISM”
– As an example of what you should do
• Hand out “Laboratory experiment:
analyzing a simple parallel plate capacitor”
– Provided as ref for analysis section
– Also you are responsible for the content of
this section
– Discuss in class
– Do demo to quantify charge of the wand
6 oct: More practice with fields, isopotential lines, and charges
•
http://vnatsci.ltu.edu/s_schneider/physlets/main/equipotentials.shtml
•
What isopotential line is missing: show it with
test charge
•
Is length of force vector on ptc
always constant along the isopotential line?
•
Do prob 17:63 for unequal like charges. Show
elevation plot of V.
Back to lightning
• What is breakdown voltage in air?
• Why does Wimshurst spark way lower
than that?
• Why does lightning strike a high object?
• What do the field lines look like?
• What will the potential be near the tree?
Quiz Friday 7 oct
• Three charges in a row. +4, -8, +4
• Draw field lines, 4 from the +4 charge
• Draw isopotential lines, 3 lines each
charge
• On separate figure, draw elevation V vs. r
Quiz 15 oct
• Estimate (dimensions approximate) the
capacitance of the leyden jar in the
Wimshurst generator.
• Estimate the charge Q stored when the
electrodes deliver a 10cm spark = 30,000V
• ANSWERS HERE….
•
A = 0.15m 2. k = 5 for glass. C = 4x10-10 F. Q = 16 mC
Classics chapter 17
•
•
•
•
•
•
•
•
Capacitor charged
Define capacitor
Experimental write-up analysis of plot
Lightning
Parallel capacitors
Charges on a line find E, V lines; plot V
draw potential lines to scale
Accelerate an e- in a field, CRT
Review for exams
•
•
•
•
Main concepts
Classic problems
Questions?
A few points that might be weak
– Graphical interpretation of simple laws Q=CV, C =
keA/d
– Difference between PE and potential, V
– Remember when mechanical energy is conserved
– Which V equations are for point charge or capacitor
– That PE and U are same thing (!!!!)
– How to recognize when Q is constant in a capacitor
A potential problem
• A 2.0C bowling ball of mass 3.0kg starts in
this room at v=0, V=250V and ends up
10.0m north of the starting point at V=30V
after travelling 290m along a indirect path.
It ends with v = 10.0m/s. Draw a picture of
the before and after situation.
• What is the energy change of the ball?
• What is the average frictional force along
the path?
•
½ m v2 – 0 + q(Vf – Vi) = Ff d
•
1.0N
Some questions for final review; may
• Sketch and explain how lightning works
• Why does lightning send static to a car
radio? Why is AM more affected than
FM?
• I have two 40W bulbs. What is power
output if I put them in parallel? Series?