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Chapter 16
Electric Charge and
   Electric Field
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?
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.
Electric charge and electric field
• 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.
• 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.
• Demonstration #4

• 1. What happens when your touch the
  electroscope with the glass rod?
Electric charge and electric field
Sample Problem

   A certain static discharge delivers -0.5
       Coulombs of electrical charge.

• How many electrons are in this discharge?
Sample Problem

1. How much positive charge resides in two moles of
hydrogen gas (H2)?



2. How much negative charge?




3. How much net charge?
Sample Problem (end 1)
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?
Coulomb’s Law and
 Electrical Force

     Day 2
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
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?
Sample Problem

Calculate the mass of ball B, which is suspended in
midair.
Electric charge and electric field
Sample Problem

• What is the force on the 4 μC charge?
Sample Problem end 2

• What is the force on the 4 μC charge?
The Electric Field
     Day 3
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Sample Problem end 3

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?
Superposition
   Day 4
Sample Problem

A proton traveling at 440 m/s in the +x direction enters
an electric field of magnitude 5400 N/C directed in the
+y direction. Find the acceleration.
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?
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?
Sample Problem end 4

What is the charge on the bead? It’s mass is 32 mg.
Electric Potential and
  Potential Energy

       Day 5
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Chapter 17
Electric Potential
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Sample Problem

A 3.0 μC charge is moved through a potential difference
of 640 V. What is its potential energy change?
Electrical Potential in Uniform Electric Fields

The electric potential is related in a simple way to a
uniform electric field.

DV = -Ed
DV: change in electrical potential (V)
E: Constant electric field strength (N/C or V/m)
d: distance moved (m)
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?
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.
Sample Problem end 5

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? End 5
Electric Field and Shielding

          Day 6
Electric charge and electric field
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?
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?
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
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 properpotential, and draw and label 3
equipotential surfaces between the plates. You may
ignore edge effects.


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




+++++++++++++++++++++++++++++
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?
Objectives: After finishing this
   unit, you should be able to:
 • Explain and demonstrate the first law of electro-
   statics and discuss charging by contact and by
   induction.
• Write and apply Coulomb’s
  Law and apply it to problems
  involving electric forces.
• Define the electron, the
  coulomb, and the microcoulomb
  as units of electric charge.
Objectives: After finishing this
   unit you should be able to:
• Define the electric field and explain what
  determines its magnitude and direction.
• Write and apply formulas for the
  electric field intensity at known
  distances from point charges.
• Discuss electric field lines and the
  meaning of permittivity of space.
• Write and apply Gauss's law for fields around
  surfaces of known charge densities.
16.1 Static Electricity; Electric Charge
                and Its Conservation
11.1    When a rubber rod is rubbed against fur, electrons
        are removed from the fur and deposited on the rod.
                         Electrons                 negative
                         move from
                                        positive
                         fur to the                   -- --
                                         ++++
                         rubber rod.



       The rod is said to be negatively charged because of an
       excess of electrons. The fur is said to be positively
       charged because of a deficiency of electrons.
Two Negative Charges Repel
1. Charge the rubber rod by rubbing against fur.
2. Transfer electrons from rod to each pith ball.




  The two negative charges repel each other.
  The two negative charges repel each other.
The Two Types of Charge


     Rubber                         glass
                    Attraction

         fur                      silk

Note that the negatively charged (green) ball is
attracted to the positively charged (red) ball.

         Opposite Charges Attract!
         Opposite Charges Attract!
16.2 Electric Charge in the Atom

Atom:
Nucleus (small,
massive, positive
charge)
Electron cloud (large,
very low density,
negative charge)




              11.2
16.2 Electric Charge in the Atom

Atom is electrically neutral.
Rubbing charges objects by moving electrons
from one to the other.
16.2 Electric Charge in the Atom

Polar molecule: neutral overall, but charge not
evenly distributed
16.3 Insulators and Conductors


Conductor:             Insulator:
Charge flows freely    Almost no charge flows
Metals                 Most other materials
    Some materials are semiconductors.
16.4 Induced Charge; the Electroscope
Charging Spheres by Induction
                                     Induction
                        --- - -
                                      - - Electrons
                               ++
                               ++     -- Repelled

   Uncharged Spheres     Separation of Charge
--- - -
      ++
      ++
              --             +
                            + +
                                     -
                                    - -
              --             +       -

 Isolation of Spheres     Charged by Induction

                                             11.3
Induction for a Single Sphere
                                        Induction
                       --- - -
                               + ----
                             + --
                             ++ --

Uncharged Sphere         Separation of Charge

--- - -
         -- - - - -
      ++ -
      ++ -
                              +
                             + +
                              +

 Electrons move       Charged by Induction
   to ground.
The Quantity of Charge
  The quantity of charge (q) can be defined in
  terms of the number of electrons, but the
  Coulomb (C) is a better unit for later work. A
  temporary definition might be as given below:

     The Coulomb: 1 C = 6.25 x 1018 electrons
     The Coulomb: 1 C = 6.25 x 1018 electrons

Which means that the charge on a single electron is:

            1 electron: e-- = -1.6 x 10-19 C
            1 electron: e = -1.6 x 10-19 C
Units of Charge
The coulomb (selected for use with electric
currents) is actually a very large unit for static
electricity. Thus, we often encounter a need to
use the metric prefixes.


   1 µC = 1 x 10-6 C
   1 µC = 1 x 10-6 C      1 nC = 1 x 10-9 C
                          1 nC = 1 x 10-9 C


              1 pC = 1 x 10-12 C
              1 pC = 1 x 10-12 C
16.4 Induced Charge; the Electroscope

The electroscope
can be used for
detecting charge:
16.4 Induced Charge; the Electroscope
The electroscope can be charged either by
conduction or by induction.
16.4 Induced Charge; the Electroscope

The charged electroscope can then be used to
determine the sign of an unknown charge.
16.5 Coulomb’s Law

Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
11.4


             Coulomb’s Law
The force of attraction or repulsion between two
 The force of attraction or repulsion between two
point charges is directly proportional to the product
 point charges is directly proportional to the product
of the two charges and inversely proportional to the
 of the two charges and inversely proportional to the
square of the distance between them.
 square of the distance between them.

              F
    - q                q’   +
              r                         qq '
                                      F∝ 2
F                            F           r
      q                q’
      -                -
16.5 Coulomb’s Law
 The force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
Electric charge and electric field
16.5 Coulomb’s Law

Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:




 Charges produced by rubbing are
 typically around a microcoulomb:
16.5 Coulomb’s Law

Charge on the electron:




Electric charge is quantized in units
of the electron charge.
16.5 Coulomb’s Law

The proportionality constant k can also be
written in terms of   , the permittivity of free
space:




                                               (16-2)
Problem-Solving Strategies
1. Read, draw, and label a sketch showing all
   given information in appropriate SI units.
2. Do not confuse sign of charge with sign of
   forces. Attraction/Repulsion determines the
   direction (or sign) of the force.
3. Resultant force is found by considering force
   due to each charge independently. Review
   module on vectors, if necessary.
4. For forces in equilibrium: ΣFx = 0 = ΣFy = 0.
Electric charge and electric field
Electric charge and electric field
16.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces
on each charge from every other charge can be
calculated and then added as vectors.
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field
Summary of Formulas:
     Like Charges Repel; Unlike Charges Attract.
     Like Charges Repel; Unlike Charges Attract.

            kqq '                      N ⋅m 2
          F= 2              k =9 x 109
             r                          C2

     1 µC = 1 x 10-6 C
        C
     1 µ = 1 x 10-6 C       1 nC = 1 x 10-9 C
                            1 nC = 1 x 10-9 C


1 pC = 1 x 10-12 C
1 pC = 1 x 10-12 C   1 electron: e-- = -1.6 x 10-19 C
                     1 electron: e = -1.6 x 10-19 C
16.6 Solving Problems Involving
     Coulomb’s Law and Vectors


The net force on a charge is the vector
sum of all the forces acting on it.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
Vector addition review:
16.7 The Electric Field

The electric field is the
force on a small charge,
divided by the charge:



                    (16-3)
16.7 The Electric Field

For a point charge:


                             (16-4a)




                             (16-4b)




          11.5
16.7 The Electric Field

Force on a point charge in an electric field:

                                  (16-5)



Superposition principle for electric fields:
16.7 The Electric Field

Problem solving in electrostatics: electric
  forces and electric fields
1. Draw a diagram; show all charges, with
  signs, and electric fields and forces with
  directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
16.8 Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge
and end on a negative charge.
16.8 Field Lines



The number of field lines starting (ending)
on a positive (negative) charge is
proportional to the magnitude of the charge.


The electric field is stronger where the field
lines are closer together.
16.8 Field Lines
     Examples of E-Field Lines
     Two equal but             Two identical
     opposite charges.         charges (both +).




Notice that lines leave + charges and enter - charges.
Also, E is strongest where field lines are most dense.
16.8 Field Lines


 The electric field between
 two closely spaced,
 oppositely charged parallel
 plates is constant.
16.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the
  field; the field is tangent to the line.
2. The magnitude of the field is proportional
  to the density of the lines.
3. Field lines start on positive charges and
  end on negative charges; the number is
  proportional to the magnitude of the
  charge.
16.9 Electric Fields and Conductors
The static electric field inside a conductor is
zero – if it were not, the charges would move.




The net charge on a conductor is on its
surface.
16.9 Electric Fields and Conductors

                 The electric field is
                 perpendicular to the
                 surface of a conductor –
                 again, if it were not,
                 charges would move.
16.10 Gauss’s Law
          Electric flux:
                             11.6




                           (16-7)


       Electric flux 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 situations with a high degree of
symmetry.
The Density of Field Lines
 Gauss’s Law: The field E at any point in space
Gauss’s Law: The field E at any point in space
 is proportional to the line density σ at that point.
is proportional to the line density σ at that point.

  Gaussian Surface            Line density σ     ∆N

                 r

                                          ∆A

                                                  ∆N
                                               σ=
      Radius r                                    ∆A
Gauss’s Law
 Gauss’s Law: The net number of electric field
  Gauss’s Law: The net number of electric field
 lines crossing any closed surface in an outward
  lines crossing any closed surface in an outward
 direction is numerically equal to the net total
  direction is numerically equal to the net total
 charge within that surface.
  charge within that surface.

              N = Σε 0 EA = Σq

If we represent q as net enclosed          q
positive charge, we can write        ΣEA =
rewrite Gauss’s law as:                    ε0
Electric charge and electric field
Electric charge and electric field
Electric charge and electric field

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Electric charge and electric field

  • 1. Chapter 16 Electric Charge and Electric Field
  • 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.
  • 5. • 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.
  • 6. • 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.
  • 7. • Demonstration #4 • 1. What happens when your touch the electroscope with the glass rod?
  • 9. Sample Problem A certain static discharge delivers -0.5 Coulombs of electrical charge. • How many electrons are in this discharge?
  • 10. Sample Problem 1. How much positive charge resides in two moles of hydrogen gas (H2)? 2. How much negative charge? 3. How much net charge?
  • 11. Sample Problem (end 1) 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?
  • 12. Coulomb’s Law and Electrical Force Day 2
  • 17. 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?
  • 18. Sample Problem Calculate the mass of ball B, which is suspended in midair.
  • 20. Sample Problem • What is the force on the 4 μC charge?
  • 21. Sample Problem end 2 • What is the force on the 4 μC charge?
  • 31. Sample Problem end 3 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?
  • 32. Superposition Day 4
  • 33. Sample Problem A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration.
  • 34. 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?
  • 35. 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?
  • 36. Sample Problem end 4 What is the charge on the bead? It’s mass is 32 mg.
  • 37. Electric Potential and Potential Energy Day 5
  • 55. Sample Problem A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change?
  • 56. Electrical Potential in Uniform Electric Fields The electric potential is related in a simple way to a uniform electric field. DV = -Ed DV: change in electrical potential (V) E: Constant electric field strength (N/C or V/m) d: distance moved (m)
  • 57. 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?
  • 58. 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.
  • 59. Sample Problem end 5 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? End 5
  • 60. Electric Field and Shielding Day 6
  • 62. 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?
  • 63. 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?
  • 69. 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 properpotential, and draw and label 3 equipotential surfaces between the plates. You may ignore edge effects. -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +++++++++++++++++++++++++++++
  • 70. 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?
  • 71. Objectives: After finishing this unit, you should be able to: • Explain and demonstrate the first law of electro- statics and discuss charging by contact and by induction. • Write and apply Coulomb’s Law and apply it to problems involving electric forces. • Define the electron, the coulomb, and the microcoulomb as units of electric charge.
  • 72. Objectives: After finishing this unit you should be able to: • Define the electric field and explain what determines its magnitude and direction. • Write and apply formulas for the electric field intensity at known distances from point charges. • Discuss electric field lines and the meaning of permittivity of space. • Write and apply Gauss's law for fields around surfaces of known charge densities.
  • 73. 16.1 Static Electricity; Electric Charge and Its Conservation 11.1 When a rubber rod is rubbed against fur, electrons are removed from the fur and deposited on the rod. Electrons negative move from positive fur to the -- -- ++++ rubber rod. The rod is said to be negatively charged because of an excess of electrons. The fur is said to be positively charged because of a deficiency of electrons.
  • 74. Two Negative Charges Repel 1. Charge the rubber rod by rubbing against fur. 2. Transfer electrons from rod to each pith ball. The two negative charges repel each other. The two negative charges repel each other.
  • 75. The Two Types of Charge Rubber glass Attraction fur silk Note that the negatively charged (green) ball is attracted to the positively charged (red) ball. Opposite Charges Attract! Opposite Charges Attract!
  • 76. 16.2 Electric Charge in the Atom Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge) 11.2
  • 77. 16.2 Electric Charge in the Atom Atom is electrically neutral. Rubbing charges objects by moving electrons from one to the other.
  • 78. 16.2 Electric Charge in the Atom Polar molecule: neutral overall, but charge not evenly distributed
  • 79. 16.3 Insulators and Conductors Conductor: Insulator: Charge flows freely Almost no charge flows Metals Most other materials Some materials are semiconductors.
  • 80. 16.4 Induced Charge; the Electroscope Charging Spheres by Induction Induction --- - - - - Electrons ++ ++ -- Repelled Uncharged Spheres Separation of Charge --- - - ++ ++ -- + + + - - - -- + - Isolation of Spheres Charged by Induction 11.3
  • 81. Induction for a Single Sphere Induction --- - - + ---- + -- ++ -- Uncharged Sphere Separation of Charge --- - - -- - - - - ++ - ++ - + + + + Electrons move Charged by Induction to ground.
  • 82. The Quantity of Charge The quantity of charge (q) can be defined in terms of the number of electrons, but the Coulomb (C) is a better unit for later work. A temporary definition might be as given below: The Coulomb: 1 C = 6.25 x 1018 electrons The Coulomb: 1 C = 6.25 x 1018 electrons Which means that the charge on a single electron is: 1 electron: e-- = -1.6 x 10-19 C 1 electron: e = -1.6 x 10-19 C
  • 83. Units of Charge The coulomb (selected for use with electric currents) is actually a very large unit for static electricity. Thus, we often encounter a need to use the metric prefixes. 1 µC = 1 x 10-6 C 1 µC = 1 x 10-6 C 1 nC = 1 x 10-9 C 1 nC = 1 x 10-9 C 1 pC = 1 x 10-12 C 1 pC = 1 x 10-12 C
  • 84. 16.4 Induced Charge; the Electroscope The electroscope can be used for detecting charge:
  • 85. 16.4 Induced Charge; the Electroscope The electroscope can be charged either by conduction or by induction.
  • 86. 16.4 Induced Charge; the Electroscope The charged electroscope can then be used to determine the sign of an unknown charge.
  • 87. 16.5 Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.
  • 88. 11.4 Coulomb’s Law The force of attraction or repulsion between two The force of attraction or repulsion between two point charges is directly proportional to the product point charges is directly proportional to the product of the two charges and inversely proportional to the of the two charges and inversely proportional to the square of the distance between them. square of the distance between them. F - q q’ + r qq ' F∝ 2 F F r q q’ - -
  • 89. 16.5 Coulomb’s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.
  • 91. 16.5 Coulomb’s Law Unit of charge: coulomb, C The proportionality constant in Coulomb’s law is then: Charges produced by rubbing are typically around a microcoulomb:
  • 92. 16.5 Coulomb’s Law Charge on the electron: Electric charge is quantized in units of the electron charge.
  • 93. 16.5 Coulomb’s Law The proportionality constant k can also be written in terms of , the permittivity of free space: (16-2)
  • 94. Problem-Solving Strategies 1. Read, draw, and label a sketch showing all given information in appropriate SI units. 2. Do not confuse sign of charge with sign of forces. Attraction/Repulsion determines the direction (or sign) of the force. 3. Resultant force is found by considering force due to each charge independently. Review module on vectors, if necessary. 4. For forces in equilibrium: ΣFx = 0 = ΣFy = 0.
  • 97. 16.5 Coulomb’s Law Coulomb’s law strictly applies only to point charges. Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors.
  • 102. Summary of Formulas: Like Charges Repel; Unlike Charges Attract. Like Charges Repel; Unlike Charges Attract. kqq ' N ⋅m 2 F= 2 k =9 x 109 r C2 1 µC = 1 x 10-6 C C 1 µ = 1 x 10-6 C 1 nC = 1 x 10-9 C 1 nC = 1 x 10-9 C 1 pC = 1 x 10-12 C 1 pC = 1 x 10-12 C 1 electron: e-- = -1.6 x 10-19 C 1 electron: e = -1.6 x 10-19 C
  • 103. 16.6 Solving Problems Involving Coulomb’s Law and Vectors The net force on a charge is the vector sum of all the forces acting on it.
  • 104. 16.6 Solving Problems Involving Coulomb’s Law and Vectors Vector addition review:
  • 105. 16.7 The Electric Field The electric field is the force on a small charge, divided by the charge: (16-3)
  • 106. 16.7 The Electric Field For a point charge: (16-4a) (16-4b) 11.5
  • 107. 16.7 The Electric Field Force on a point charge in an electric field: (16-5) Superposition principle for electric fields:
  • 108. 16.7 The Electric Field Problem solving in electrostatics: electric forces and electric fields 1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions 2. Calculate forces using Coulomb’s law 3. Add forces vectorially to get result
  • 109. 16.8 Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.
  • 110. 16.8 Field Lines The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together.
  • 111. 16.8 Field Lines Examples of E-Field Lines Two equal but Two identical opposite charges. charges (both +). Notice that lines leave + charges and enter - charges. Also, E is strongest where field lines are most dense.
  • 112. 16.8 Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant.
  • 113. 16.8 Field Lines Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. The magnitude of the field is proportional to the density of the lines. 3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.
  • 114. 16.9 Electric Fields and Conductors The static electric field inside a conductor is zero – if it were not, the charges would move. The net charge on a conductor is on its surface.
  • 115. 16.9 Electric Fields and Conductors The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.
  • 116. 16.10 Gauss’s Law Electric flux: 11.6 (16-7) Electric flux through an area is proportional to the total number of field lines crossing the area.
  • 117. 16.10 Gauss’s Law Flux through a closed surface:
  • 118. 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 situations with a high degree of symmetry.
  • 119. The Density of Field Lines Gauss’s Law: The field E at any point in space Gauss’s Law: The field E at any point in space is proportional to the line density σ at that point. is proportional to the line density σ at that point. Gaussian Surface Line density σ ∆N r ∆A ∆N σ= Radius r ∆A
  • 120. Gauss’s Law Gauss’s Law: The net number of electric field Gauss’s Law: The net number of electric field lines crossing any closed surface in an outward lines crossing any closed surface in an outward direction is numerically equal to the net total direction is numerically equal to the net total charge within that surface. charge within that surface. N = Σε 0 EA = Σq If we represent q as net enclosed q positive charge, we can write ΣEA = rewrite Gauss’s law as: ε0