Do Now (11/11/13):

1
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!

2
Electrostatics
3
Bad Hair Day
4
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.
5
Charges That Things Accumulate

• 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

• Very positive
• Human hands (usually too moist, though)
• Rabbit Fur
• Glass
• Human hair
• Nylon
• Wool
• Fur
• Lead
• Silk
• Aluminum
• Paper
• Cotton
• Steel
• Neutral

6
Charging an Object by Touching
Two Objectsone is charged

Objects touchcharge is transferred

Objects separateboth are charged


7
Behavior of Electric Charges
8
Charging an Electroscope
An electroscope is a device that permits us to
explore the concepts of induction and conduction
charging.
9
Charging by Contact
Some electrons leave rod and spread over sphere.
10
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.
11
Charge Distributions
Charge on Metal Points
Charge on Insulators
Charge on Metals
 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.
12
Charges on a Conductor
13
Attracting Uncharged Metallic Objects
 Nuclei remain in place electrons move to
bottom.
Electrons are free to  move  in metals.
14
Charges on an Insulator
15
Attracting Uncharged Nonmetallic Objects
16
Charges Accumulate on Points
17
A Shocking Experience
18
How Lightning Occurs
19
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.

20
Applications of Electrostatic Charging
Negatively charged paint adheres to positively
charged metal.
Fine mist of negatively charged goldparticles
adhere to positively chargedprotein on
fingerprint.
21
Electrostatic Air Cleaner
22
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
23
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)
24
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 (1/4pe0) (Q1Q2/r2) where e0 is the
  permittivity of free space 1/4pk
• 8.85 x 10-12 C2/Nm2

25
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
26
Simple Force Calculation
 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. 
What is the force between the charges? If the two
charges are of opposite sign, what is the
direction of the force? 
27
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?
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Three Charges on a Line  Part I
 Force between any two charges F
kq1q2/r2-----------------------------------------
----------------------- 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  
Where may any test charge q be placed between the
charges if it is to experience zero electric
force?
29
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?
30
How Lightning Occurs
31
Electric Force Vectors
Consider the forces exerted on the charge in the
top right by the other three
                                                  
               
32
Electric Fields Produce Forces
33
The Electric Field Due to a Point Charge
F kQq0/r2        Define  E F/q0 kQ/r2
34
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
• r2

q
35
Electric Fields
Electric field due to a negative point
charge.------------------------------------Arro
ws point towardnegative charge.Field is
sphericallysymmetric.
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
36
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

37
E-Field of Spherical Charge Distributions

• 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)

E kQ/r2 (9x109)(5)/22                
1.125 x 1010 N/C
38
Electric Field Calculation
E2 (3.0)2 (2.0)2      13.0E 3.61 N/Cq
tan-1(2/3)    33.7 degrees
39
Symmetry In Electric Field  Calculations
40
Electric Field of Dipoles
41
Electric Fields Under the Sea
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
Elephant Gnathonemus detects nearby objects by
their effects on the electric field.
42
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 positive
• This is consistent with the force on a POSITIVE
  test charge

43
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
44
Practice

• Complete Problem 10 and 11 in your textbook in
  Chapter 15

45
Do Now (11/13/13)

• Pick up a green/yellow half sheet from the back
  of the room on your way in
• Review yesterdays Do Now (the solution is on the
  back board)

46
A Parallel Plate Capacitor
Example  A 0.15 m2  q   6 x 10-6 C  s  
 q/A        6 x 10-6 C/              0.15 m2 
     40 x 10-6 C/m2  E  s/e0    40 x
10-6/         8.85 x 10-12     4.52 x 106 N/C
s  q/A  charge densityE  s/e0    e0 8.85
x 10-12 N-m2/C2e0 is called the "permittivity of
vacuum"
47
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.

48
Electric Field Inside a Conductor
If E weren't zero inside, thefree electrons (not
shown)would accelerate.
Excess charge inside a metal moves to the
surface.  
At equilibrium, all excess charge on a metal
resides on the    surface of the metal.
49
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 FqE. 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

50
Electric Fields and Conductors (contd)

• A charge placed inside a conducting sphere
  results in charges as shown in the figure

51
Electric Fields and Conductors (contd)

• 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.

52
E-Field is Perpendicular to Conductors in
Equilibrium
53
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?
54
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

55
Recognizing Incorrect Electric Field Patterns
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.
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.
56
Using Metal to Shield Electronic Components
57
Electric Flux Through a Plane Surface
Electric Flux F EA cos q
58
Electric Flux Through a Closed Surface
Electric Flux F E DA cos q (Some texts use
DS 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.
59
Electric 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

In the left figure, the flux is zero.
In the right figure, the flux is 2.
60
Gauss's Law    
Friedrich Gauss (1777-1855)Gauss's LawS AE
cosq q/e0
q net charge inside Gaussian surface This is
useful if q 0 and E constant.
61
Gauss Law

• Where 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

62
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.
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64
Gauss Michael Faraday
Faraday 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.
He verified all of this because he DID NOT get
shocked while INSIDE the box. This is called
Faradays cage.
65
Gausss Law

• For Physics B E-field inside a conductor is zero

66
For Closed Surfaces
67
Calculus
68
Gauss's Law Gives Field Due to a Point Charge
Gauss's Law SAE cosq q/e0               A
area of sphere       4pr2  E  is the same at
all points  on the surface         q 0  cos
q 1  (4pr2)E q/e0          E
q/(4pe0r2) 
69
Gauss's Law Application
SAE cosq q/e0q sA    where s charge
densityA1E A2 (0) A3E  sA/e02AE
 sA/e0E s/2e0
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.
70
Gauss Law How does it work?
Consider a POSITIVE POINT CHARGE, Q.

• Step 1 Is there a source of symmetry?

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.
The E is then brought out of the integral.
71
Gauss Law How does it work?
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.
Step 4 Identify the charge enclosed?
The charge enclosed is Q!
This is the equation for a POINT CHARGE!
72
Cylinder with Charge distribution

• Charge distribution

73
Gauss Law and cylindrical symmetry
Consider 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.












This is the same equation we got doing extended
charge distributions.
74
Gauss Law for insulating sheets and disks

• A 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.

This is the same equation we got doing extended
charge distributions.
75
Gauss Law for conducting sheets and disks

• A 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


E 0





76
In summary

• Whether you use electric charge distributions or
  Gauss Law you get the SAME electric field
  functions for symmetrical situations.

Function Point, hoop, or Sphere (Volume) Disk or Sheet (AREA) insulating and thin Line, rod, or cylinder (LINEAR)
Equation
77
Practice

• Complete the multiple choice questions in Chapter
  15

78
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 s
E is zero at the left end and E is parallel to
the side. q sA      EA sA/e0 E s/e0
79
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".

80
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.

81
Van de Graaff Generator
82
Van de Graaff Generator
83
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

84
Cereal Storm
85
Van de Graaff Generator

1. Output terminalan aluminum or steel sphere
2. Upper BrushA piece of fine metal wire
3. Upper RollerA piece of nylon
4. Belt--A piece of tubing
5. Power supply
6. Lower Brush
7. Lower rollernylon covered with silicon tape

86
Do Now (11/18/13)

• Define the following in your own words. If you do
  not know, hypothesize
• Capacitance
• Voltage
• Potential

87
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

88
Brainstorm

• The charges that flow through the wires in your
  home ____.
• are stored in the outlets at your home
• are created when an appliance is turned on
• originate at the power (energy) company
• originate in the wires between your home and the
  power company
• already exist in the wires at your home

89
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
90
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

91
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

92
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

93
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

94
Equipotential Examples 1
Equipotential lines are perpendicular to the
electric field lines
The potential along an equipotential curve is the
same at any point
95
Equipotential Examples 2
V W/qmoved
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.
As we move a charge from one equipotential line
to another we change its electric potential
96
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

97
Electric Potential of a Point Charge

• The electric potential at a distance r from a
  point charge Q is given by
• V (1/4pe0) (Q/r)
• k (Q/r)
• V goes to zero as r ? 8

98
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 8)
  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)

99
Which Has the Most Potential Energy?
Largest negative energy Hardest to separate
Positive energy
100
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

101
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 e0A/d

102
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 Ke0A/d or C eA/d where e Ke0

103
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

104
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
  cant 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

105
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

106
Common Dielectric Constants
107
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?

108
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

109
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

110
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

111
Do Now (11/19/13)

• Draw a parallel circuit
• Draw a series circuit
• What is the difference between the two?

112
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

113
How Lightning Occurs
114
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. 

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Practice

• Complete the multiple choice questions in Ch. 16