Charge and Polarization

1

• Charge and Polarization

2
Demonstration 1

1. Demonstrate how you can pick up the tissue
   without touching it in any way with your body.
2. What is occurring on the atomic level that lets
   you do this?

3
The atom

• The atom has positive charge in the nucleus,
  located in the protons. The positive charge
  cannot move from the atom unless there is a
  nuclear reaction.
• The atom has negative charge in the electron
  cloud on the outside of the atom. Electrons can
  move from atom to atom without all that much
  difficulty.

4
Question

• You charge the balloon by rubbing it on hair or
  on a sweater, and the balloon becomes negative.
  How can it pick up a neutral tissue?

5
This is an electroscope
Pole
The electroscope is made from a metal or other
conductor, and may be contained within a
flask. The vanes are free to move.
Vanes
6
Demonstration 2

1. Rub the black rod with the fur. Bring the rod
   toward the pole of the electroscope. What happens
   to the vanes?
2. Come up with an atomic-level explanation for your
   observations.

7
Demonstration 3

1. Rub the glass rod with the silk. Bring the rod
   toward the pole of the electroscope. What happens
   to the vanes?
2. Come up with an atomic-level explanation for your
   observations.

8
Demonstration 4

1. What happens when your touch the electroscope
   with the glass rod?

9
Charge

• Charge comes in two forms, which Ben Franklin
  designated as positive () and negative().
• Charge is quantized.
• The smallest possible stable charge, which we
  designate as e, is the magnitude of the charge on
  1 electron or 1 proton.
• We say a proton has charge of e, and an electron
  has a charge of e.
• e is referred to as the elementary charge.
• e 1.602 ? 10-19 Coulombs.
• The coulomb is the SI unit of charge.

10
Sample Problem

• A certain static discharge delivers -0.5 Coulombs
  of electrical charge. How many electrons are in
  this discharge?

11

• Sample Problem
• A certain static discharge delivers -0.5 Coulombs
  of electrical charge.
• How many electrons are in this discharge?
• q n e
• n q / e
• n (-0.5 C) / (-1.602 x 10-19 C)
• n 3,121,098,626,716,604,245

12
Sample Problem

• How much positive charge resides in two moles of
  hydrogen gas (H2)?
• How much negative charge?
• How much net charge?

13
Sample Problem

• The total charge of a system composed of 1800
  particles, all of which are protons or electrons,
  is 31x10-18 C.
• How many protons are in the system?
• How many electrons are in the system?

14

• Coulombs Law and Electrical Force

15
Electric Force

• Charges exert forces on each other.
• Like charges (two positives, or two negatives)
  repel each other, resulting in a repulsive force.
• Opposite charges (a positive and a negative)
  attract each other, resulting in an attractive
  force.

16
Coulombs Law form 1

• Coulombs law tells us how the magnitude of the
  force between two particles varies with their
  charge and with the distance between them.
• k 8.99 ? 109 N m2 / C2
• q1, q2 are charges (C)
• r is distance between the charges (m)
• F is force (N)
• Coulombs law applies directly only to
  spherically symmetric charges.

17
Coulombs Law form 2

• Sometimes you see Coulombs Law written in a
  slightly different form
• eo 8.85 ? 10-12 C2/ N m2
• q1, q2 are charges (C)
• r is distance between the charges (m)
• F is force (N)
• This version is theoretically derived and less
  practical that form 1

18
Spherically Symmetric Forces

• Newtons Law of Gravity
• Coulombs Law

19
Sample Problem

• A point charge of positive 12.0 µC experiences an
  attractive force of 51 mN when it is placed 15 cm
  from another point charge. What is the other
  charge?

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Sample Problem

• Calculate the mass of ball B, which is suspended
  in midair.

qA 1.50 nC
A
1.3 m
B
qB -0.50 nC
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Superposition

• Electrical force, like all forces, is a vector
  quantity.
• If a charge is subjected to forces from more than
  one other charge, vector addition must be
  performed.
• Vector addition to find the resultant vector is
  sometimes called superposition.

24
Sample Problem

• What is the force on the 4 mC charge?

y (m)
2.0
1.0
2 mC
-3 mC
4 mC
2.0
1.0
x (m)
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Sample Problem

• What is the force on the 4 mC charge?

y (m)
2.0
-3 mC
1.0
2 mC
4 mC
2.0
1.0
x (m)
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28

• The Electric Field

29
The Electric Field

• The presence of or charge modifies empty
  space. This enables the electrical force to act
  on charged particles without actually touching
  them.
• We say that an electric field is created in the
  space around a charged particle or a
  configuration of charges.
• If a charged particle is placed in an electric
  field created by other charges, it will
  experience a force as a result of the field.
• Sometimes we know about the electric field
  without knowing much about the charge
  configuration that created it.
• We can easily calculate the electric force from
  the electric field.

30
Why use fields?

• Forces exist only when two or more particles are
  present.
• Fields exist even if no force is present.
• The field of one particle only can be calculated.

31
Field around charge

• The arrows in a field are not vectors, they are
  lines of force.
• The lines of force indicate the direction of the
  force on a positive charge placed in the field.
• Negative charges experience a force in the
  opposite direction.

32
Field around - charge
33
Field between charged plates


- - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - -
34
Field Vectors from Field Lines

• The electric field at a given point is not the
  field line itself, but can be determined from the
  field line.
• The electric field vectors is always tangent to
  the line of force at that point.
• Vectors of any kind are never curvy!

35
Field Vectors from Field Lines
36
Force from Electric Field

• The force on a charged particle placed in an
  electric field is easily calculated.
• F E q
• F Force (N)
• E Electric Field (N/C)
• q Charge (C)

37
Sample Problem

• The electric field in a given region is 4000 N/C
  pointed toward the north. What is the force
  exerted on a 400 µg styrafoam bead bearing 600
  excess electrons when placed in the field?

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Sample Problem

• A 400 µg styrofoam bead has 600 excess electrons
  on its surface. What is the magnitude and
  direction of the electric field that will suspend
  the bead in midair?

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41

• Superposition

42
Sample Problem

• A proton traveling at 440 m/s in the x direction
  enters an an electric field of magnitude 5400 N/C
  directed in the y direction. Find the
  acceleration.

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For Spherical Electric Fields

• The Electric Field surrounding a point charge or
  a spherical charge can be calculated by
• E k q / r2
• E Electric Field (N/C)
• k 8.99 x 109 N m2/C2
• q Charge (C)
• r distance from center of charge q (m)
• Remember that k 1/4peo

45
Principle of Superposition

• When more than one charge contributes to the
  electric field, the resultant electric field is
  the vector sum of the electric fields produced by
  the various charges.
• Again, as with force vectors, this is referred to
  as superposition.

46
Remember

• Electric field lines are NOT VECTORS, but may be
  used to derive the direction of electric field
  vectors at given points.
• The resulting vector gives the direction of the
  electric force on a positive charge placed in the
  field.

47
Sample Problem

• A particle bearing -5.0 µC is placed at -2.0 cm,
  and a particle bearing 5.0 µC is placed at 2.0
  cm. What is the field at the origin?

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Sample Problem

• A particle bearing 10.0 mC is placed at the
  origin, and a particle bearing 5.0 mC is placed
  at 1.0 m. Where is the field zero?

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Sample Problem

• What is the charge on the bead? Its mass is 32
  mg.

E 5000 N/C
40o
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53

• Electric Potential and Potential Energy

54
Electric Potential Energy

• Electrical potential energy is the energy
  contained in a configuration of charges. Like all
  potential energies, when it goes up the
  configuration is less stable when it goes down,
  the configuration is more stable.
• The unit is the Joule.

55
Electric Potential Energy

• Electrical potential energy increases when
  charges are brought into less favorable
  configurations

?U gt 0


-

56
Electric Potential Energy

• Electrical potential energy decreases when
  charges are brought into more favorable
  configurations.

?U lt 0

-


57
Electric Potential Energy


?U ____
?U ____



-
Work must be done on the charge to increase the
electric potential energy.
58
Work and Charge

• For a positive test charge to be moved upward a
  distance d, the electric force does negative
  work.
• The electric potential energy has increased and
  ?U is positive(U2 gt U1)

d

E
F
59
Work and Charge

• If a negative charge is moved upward a distance
  d, the electric force does positive work.
• The change in the electric potential energy ?U is
  negative (U2 lt U1)

-
d
F
-
E
60
Electric Potential

• Electric potential is hard to understand, but
  easy to measure.
• We commonly call it voltage, and its unit is
  the Volt.
• 1 V 1 J/C
• Electric potential is easily related to both the
  electric potential energy, and to the electric
  field.

61
Electrical Potential and Potential Energy

• The change in potential energy is directly
  related to the change in voltage.
• ?U q?V
• ?U change in electrical potential energy (J)
• q charge moved (C)
• ?V potential difference (V)
• All charges will spontaneously go to lower
  potential energies if they are allowed to move.

62
Electrical Potential and Potential Energy

• Since all charges try to decrease UE, and DUE
  qDV, this means that spontaneous movement of
  charges result in negative DU.
• ?V ?U / q
• Positive charges like to DECREASE their potential
  (DV lt 0)
• Negative charges like to INCREASE their
  potential. (DV gt 0)

63
Sample Problem

• A 3.0 µC charge is moved through a potential
  difference of 640 V. What is its potential energy
  change?

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Electrical Potential in Uniform Electric Fields

• The electric potential is related in a simple way
  to a uniform electric field.
• ?V -Ed
• ?V change in electrical potential (V)
• E Constant electric field strength (N/C or V/m)
• d distance moved (m)

d
E
DV
66
Sample Problem

• An electric field is parallel to the x-axis. What
  is its magnitude and direction of the electric
  field if the potential difference between x 1.0
  m and x 2.5 m is found to be 900 V?

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Sample Problem

• What is the voltmeter reading between A and B?
  Between A and C? Assume that the electric field
  has a magnitude of 400 N/C.

y(m)
C
1.0
A
B
1.0
2.0
x(m)
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Sample Problem

• How much work would be done BY THE ELECTRIC FIELD
  in moving a 2 mC charge from A to C? From A to B?
  from B to C?. How much work would be done by an
  external force in each case?

y(m)
C
1.0
A
B
1.0
2.0
x(m)
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72

• Electric Field Lines and Shielding

73
Lab Electric Fields and Equipotential Lines

• Java Simulation
• http//phet.colorado.edu/new/simulations/sims.php?
  simCharges_and_Fields

74
Excess Charges on Conductors

• Excess charges reside on the surface of a charged
  conductor.
• If excess charges were found inside a conductor,
  they would repel one another until the charges
  were as far from each other as possible the
  surface!

75
Electric Field and Lightning Rods

• Electric field lines are more dense near a sharp
  point, indicating the electric field is more
  intense in such regions.
• All lightning rods take advantage of this by
  having a sharply pointed tip.
• During an electrical storm, the electric field at
  the tip becomes so intense that charge is given
  off into the atmosphere, discharging the area
  near a house at a steady rate and preventing a
  sudden blast of lightning.

76
Electric Field inside a Conductor

• The electric field inside a conductor must be
  zero.

E 0






77
Conductor in an electric field

• If a conductor is placed in an electric field,
  then the charges polarize to nullify the external
  field.

-
-

-

-

E 0

-

-

-

-
78

• Energy Conservation in Electric Fields

79
Conservation of Energy Review

• In a conservative system, energy changes from one
  form of mechanical energy to another.
• When only the conservative electrostatic force is
  involved, a charged particle released from rest
  in an electric field will move so as to lose
  potential energy and gain an equivalent amount of
  kinetic energy.
• The change in electrical potential energy can be
  calculated by
• DUE qDV.

80
Sample Problem

• If a proton is accelerated through a potential
  difference of -2,000 V, what is its change in
  potential energy?
• How fast will this proton be moving if it started
  at rest?

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Sample Problem

• A proton at rest is released in a uniform
  electric field. How fast is it moving after it
  travels through a potential difference of -1200
  V? How far has it moved?

83
Electric Potential Energy for Spherical Charges

• Electric potential energy is a scalar, like all
  forms of energy.
• U kq1q2/r
• U electrical potential energy (J)
• k 8.99 ? 109 N m2 / C2
• q1, q2 charges (C)
• r distance between centers (m)
• This formula only works for spherical charges or
  point charges.

84
Drawing Parallels

• Gravitation

• Electrostatics

85
Sample Problem

• What is the potential energy of the configuration
  shown below?

y (m)
2.0
1.0
2 mC
4 mC
x (m)
2.0
1.0
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Sample Problem

• How much work was done in assembling the charge
  configuration shown below?

y (m)
2.0
-3 mC
1.0
2 mC
4 mC
x (m)
2.0
1.0
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• Potential and Potential Energy of Configurations
  of Point Charges

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Absolute Electric Potential (spherical)

• For a spherical or point charge, the electric
  potential can be calculated by the following
  formula
• V kq/r
• V potential (V)
• k 8.99 x 109 N m2/C2
• q charge (C)
• r distance from the charge (m)
• Remember, k 1/(4peo)

91
Sample Problem

• What is the electric potential at (2,2)?

y (m)
2.0
-3 mC
1.0
2 mC
4 mC
x (m)
2.0
1.0
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Equipotential surfaces
positive
negative
94
Equipotential surfaces
95
Question

• What can you say about the intersection between
  field lines and equipotential surfaces?

96
Sample Problem

• Draw field lines for the charge configuration
  below. The field is 600 V/m, and the plates are 2
  m apart. Label each plate with its proper
  potential, and draw and label 3 equipotential
  surfaces between the plates. You may ignore edge
  effects.

- - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - -


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Sample Problem

• Draw a negative point charge of -Q and its
  associated electric field. Draw 4 equipotential
  surfaces such that DV is the same between the
  surfaces, and draw them at the correct relative
  locations. What do you observe about the spacing
  between the equipotential surfaces?

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Fill in the following table for spherical charges
Force Potential Energy
Field Potential
101
What is magnitude and direction of electric
field?b) What is shortest distance one can go to
undergo a change of 5.00 V?
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