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Electric Charges and Fields

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					Electric Charges and Fields

   Pages 628 - 653
Introduction

    Electricity in one form or another
     underlies just about everything around
     you from the lightning in the sky to the
     spark when you touch someone to
     holding atoms together to form
     molecules.
Atoms

  Basic units of matter
  Made up of a nucleus surrounded by the
   shells or clouds containing electrons
Atomic Particles

  Electrons are located in the shells or
   clouds and have a negative charge.
  Protons are located in the nucleus and
   have a positive charge.
  Neutrons are located in the nucleus and
   have no charge.
Types of Materials

    There are 3 types of materials:
     Conductors, Insulators, and
     Semiconductors.
Conductors

    Conductors have electrons that are free
     to move from one atom to another within
     the material. Therefore, they DO have
     the ability to conduct electricity.
Insulators

    Insulators have electrons that are tightly
     bound to the nucleus and are not free to
     migrate. Therefore, they DO NOT have
     the ability to conduct electricity.
Semiconductors

    Semiconductors are poor conductors of
     electricity under most conditions, but
     under very specific conditions /
     environments have the ability to become
     much better conductors.
Electroscopes

  Electroscopes are devices that detect
   the presence of charge.
  Electroscopes come in 3 types: pith-ball,
   gold leaf, and moving vane.
Gold Leaf Electroscopes

  Gold leaf electroscopes show they are
   charged when their leaves diverge. This
   happens because both leaves have the
   same charge and therefore repel each
   other.
  Gold leaf electroscopes show that they
   are neutral when their leaves hang
   vertically.
Induction of a temporary charge
in an Electroscope
  Bring a positively charged rod or object
   NEAR the knob of a neutral
   electroscope.
  The excess positive charges in the rod
   attract the electrons in the electroscope.
Cont’d

  The electrons in the electroscope
   migrate up to the knob which is closest
   to the positively charged rod. The knob
   now has an excess of electrons and it is
   temporarily negatively charged.
  This migration of electrons causes only
   protons to remain in the leaves.
  Both of the leaves now have an excess
   of positive charges and repel each other.
Cont’d

  Once the charged rod is removed, the
   electrons will flow back to their original
   positions and the leaves of the electroscope
   will once again fall back to their original
   vertical positions.
  Bring a negatively charged rod or object NEAR
   the knob of a neutral electroscope.
  The excess negative charges in the rod repel
   the electrons in the knob of the electroscope.
Cont’d

  The electrons in the knob of the
   electroscope migrate down to the leaves
   which are furthest from the negatively
   charged rod. The leaves now have an
   excess of electrons and are temporarily
   negatively charged.
  Both of the leaves now have an excess
   of negative charges and repel each
   other.
Cont’d

  This migration of electrons causes only
   protons to remain in the knob which now
   has a temporary positive charge.
  Once the charged rod is removed, the
   electrons will flow back to their original
   positions and the leaves of the
   electroscope will once again fall back to
   their original vertical positions.
Polarization of a Conductor

  Bring a charged rod NEAR a conductor.
  Electrons in the conductor will migrate
   toward a positively charged rod and
   away from a negatively charged rod.
Cont’d

  This migration of electrons will leave one
   end of the conductor with a net positive
   charge and the other end with a net
   negative charge creating 2 poles, one
   positive and the other negative.
  Once the charged rod is removed, the
   electrons will drift back to their original
   positions and the whole conductor will no
   longer have poles.
Polarization of an Insulator

  Bring a charged rod NEAR an insulator.
  In an insulator the electrons are NOT
   free to migrate so the whole atom rotates
   to form an orderly arrangement that
   creates poles within the insulator.
   Polarization of Conductors and
    Insulators
Charging by Induction

  Bring a charged object NEAR a neutral
   conductor.
  “Ground” the object by connecting it with
   a conductor to a reservoir of charge such
   as the Earth. This allows electrons to
   flow either into or out of the conductor.
Cont’d

  Remove the “ground” connection.
  Remove the charged rod from the
   vicinity.
  The conductor now has a “permanent”
   charge that is opposite to the charge of
   the object brought near it.
Charging by Conduction

  TOUCH a charged object to a conductor
   / electroscope.
  If it was a negatively charged object,
   some of the excess electrons will spread
   throughout the conductor / electroscope,
   causing both objects to have the same
   negative charge.
Cont’d

    If it was a positively charged object,
     electrons from the conductor /
     electroscope will be transferred to the
     positively charged until both objects
     become equally positively charged.
Detecting Charge with a
Charged Electroscope
    When a positively charged rod is brought
     near a positively charged electroscope
     the leaves will diverge further because
     the positively charged rod causes the
     few remaining electrons to flow up to the
     rod, causing the leaves to become even
     more positively charged.
Cont’d
  When a negatively charged rod is
   brought near a negatively charged
   electroscope the leaves will diverge
   further because the negatively charged
   rod causes the electrons in the knob to
   flow down into the leaves, causing the
   leaves to become even more negatively
   charged.
  When the electroscope and charged
   object have the same charge, the leaves
   diverge further.
Cont’d

    When a positively charged rod is brought
     near a negatively charged electroscope
     the leaves will collapse back toward the
     vertical because some of the excess
     electrons in the leaves will be drawn
     back up into the knob causing the leaves
     to be less negatively charged.
Cont’d

  When a negatively charged rod is brought
   near a positively charged electroscope the
   leaves will collapse back toward the vertical
   because the few remaining electrons in the
   knob will be forced back down into the leaves
   making them less positively charged.
  When the electroscope and the charged object
   have opposite charges, the leaves will
   collapse back toward the vertical.
Static Electricity

  Static charges are charges at rest.
  There are 2 kinds: positive and
   negative.
  Like charges repel and unlike charges
   attract.
  Neutrals are attracted to all charged
   objects.
  Charges exert a force through a
   distance.
   Static Electricity

   Electrostatics Lab
Coulomb

  The unit of charge in the metric system is
   the Coulomb (C).
  It is named after Charles Coulomb a
   French physicist.
Cont’d

    A coulomb is defined as the amount of
     charge found on 6.25*1018 electrons or
     protons. Therefore, the magnitude of the
     charge of a proton or electron is 1.6*10-
     19 C. The mass of a proton is 1.67*10-27

     kg and the mass of the electron is
     9.1*10-31 kg.
Coulomb’s Law

                kq1 q 2
             F     2
                 d
 F - Force (N)
 d - distance between charged particles (m)
 q1 - Charge of first particle (C)
 q2 - Charge of second particle (C)
 k - constant of proportionality -
  9*109 Nm2/C2
 A positive force indicates repulsion.
 A negative force indicates attraction.
   Forces in a multiple charge system
Sample Problems - Coulomb’s
Law
  Calculate the net charge on a substance
   consisting of 5*1014 electrons.
  How many electrons must be removed
   from a metal sphere to give the sphere a
   net positive charge of 4.8 μC?
Cont’d

  Two point charges of magnitude 3 μC
   and 5 μC are separated by a distance of
   0.5 m. Find the electric force of
   repulsion between the two.
  A sphere with a charge of 4*10-5 C is
   attracted by a second sphere with a
   force of 350 N when the separation is 10
   cm. Calculate the charge on the second
   sphere.
Cont’d

  Two identical point charges are 3 cm apart.
   Find the charge on each of them if the force of
   repulsion is 4*10-7 N.
  Three charged spheres are located along a
   metric ruler. The 3 μC charge is located at 0
   cm, the 5 μC is located at the 5 cm mark, and
   the -15 μC charge is located at the 10 cm
   mark. Find the net force on the 5 μC charge
   and which direction will it move?
Homework Quiz 1

  1. If an object has a deficit of 500
   electrons, what is the charge on the
   object?
  2. Two pith balls are separated by a
   distance of 20 cm. They experience an
   attractive force of 2 N. If one pith ball
   has a charge of 4 micro Coulombs, what
   is the charge on the second pith ball?
Electric Fields

  Electric fields have both magnitude and
   direction.
  Lines of force show the direction that a
   positive test charge would move within the
   field.
  Electric field strength or intensity is indicated
   by the spacing between the lines. The field is
   strong where the lines are close together and
   weaker where they are further apart.
Cont’d

  Field lines always begin on a positive
   charge and end on a negative charge.
  The number of field lines drawn around a
   charge is proportional to the magnitude
   of its charge.
  No two field lines ever cross.
Cont’d

  Field lines leave and arrive at surfaces
   perpendicular to the surface since that is
   the shortest path.
  Electric field surrounding a single
   positive charge
  Electric Field surrounding a single
   negative charge
Electric Field Intensity

                   F
                E
                   q
  E - Electric Field Strength or Intensity (N/C)
  F - Force experienced by a test charge at that
   location (N)
  q - magnitude of the test charge placed at that
   location (C).
            kq1 q 2
        F    d  2    kq1
     E             2
        q    q2      d
 E – Electric Field strength or intensity (N/C)
 k – constant of proportionality (9*109)
 d –distance (m)
 q – magnitude of charge creating the field (C)
Sample Problems - Electric Field
Intensity
  The force on a charge of -3*10-7 C is
   measured and found to be 0.24 N in a
   downward direction. What are the
   magnitude and direction of the electric
   field at this point?
  Calculate the magnitude and direction of
   the electric field at a point 50 cm directly
   above a charge of -2*10-6 C.
 Electric Potential

                     kq1 q 2
                PE 
                       d
 PE - Electric Potential Energy (J)
 d - distance between charged particles (m)
 q1 - Charge of first particle (Coulomb, C)
 q2 - Charge of second particle (Coulomb, C)
 k - constant of proportionality 9*109 Nm2/C2
Electric Potential

  Electric potential is the ratio of electric
   potential energy to charge.
  Electric potential is measured in Joules
   per Coulomb otherwise known as a Volt.
  If two objects are attracted to each other
   and they are further separated, their PE
   increases but if they come closer
   together their PE decreases.
Cont’d

    If two objects are repelled by each other
     and they are further separated, their PE
     will decrease but if they come closer
     together their PE increases.
Potential Difference or Voltage

  As with gravitational potential energy,
   your frame of reference determines the
   “amount” of PE, we will only talk about
   changes in potential energy.
  The change in potential energy is called
   potential difference.
Cont’d

    If work is required to move a charge from
     one point to another, then there is a
     potential difference between the two
     locations. If NO work is required to
     move the charge from one place to
     another, then there is no potential
     difference between the two locations.
Cont’d

                   W
                V
                   q
  V - voltage or potential difference (V)
  W - work done (J)
  q – magnitude of the charge (C)
Sample Problems - Potential
Difference
  What is the potential difference between
   two points if 200 J of energy is required
   to move 40 C from one point to another?
  How much energy is required to move an
   electron between the two terminals of a
   large X-ray tube whose potential
   difference is 4 million Volts?
Cont’d

    An electron leaves the heated cathode of
     a radio or TV vacuum tube with
     negligible initial velocity, and is
     accelerated through an applied potential
     difference of 500V. What is the velocity
     of the electron as it approaches the
     electrode?
Equipotential Lines or Surfaces

  Equipotential lines or surfaces consist of
   all points around a charged object that
   have the same electric potential.
  No work is done moving along an
   equipotential line or surface.
Cont’d

  These lines or surfaces are always
   perpendicular to the lines of force at the
   point where the equipotential line or
   surface crosses the line of force.
  Equipotential lines / surfaces do not
   cross since the same point cannot have
   two different potentials.
   Equipotential Lines
Parallel Plates of Charge

  A constant electric force and field can be
   made by placing two large, flat
   conducting plates parallel to each other
   and charging them oppositely.
  The electric field between them is
   constant except at the edges of the
   plates.
Cont’d

  If an electron is placed near the
   negatively charged plate, it will
   experience a constant force as it moves
   across the open space toward the
   positively charged plate.
  The electric field between the two plates
   is said to be directed from the positive
   plate to the negative plate.
Potential Difference between two
parallel plates

             V  Ed
  V - Voltage or Potential Difference
   between the plates (V)
  E - Electric Field Intensity (N/C)
  d - distance between the plates (m)
Sample Problems - Parallel
Plates
    A 12 V battery is connected between two
     parallel metal plates separated by 0.3
     cm. Find the strength of the electric
     field.
Cont’d

    A proton is released form rest in a
     uniform electric field of magnitude 8000
     V/m. The proton undergoes a
     displacement of 0.5 m in the direction of
     the field. Find the change in the electric
     potential of the proton as a result of this
     displacement. Find the speed of the
     proton after it has been moved 0.5 m,
     starting from rest.
Electric Field Simulation Lab

    http://www.gel.ulaval.ca/~mbusque/elec/
     main_e.html
Honors Homework Quiz
 1.   A force of 0.01is required to move a charge of 7
      microCoulombs a distance of 25 cm in an electric
      field. What is the size of the potential difference
      between the points?
 2.   Two parallel metal plates have opposite charges and
      a difference of potential of 1000 V between them.
      How much work is done in moving an electron from
      the negatively charged plate to the positively
      charged plate?
 3.   A spark will jump between two people if the electric
      field exceeds 4 * 106 V/m. You shuffle across a rug
      and a spark jumps when you put your finger 0.15 cm
      from another person’s arm. Calculate the potential
      difference between your body and the other person’s
      arm.
Academic Homework Quiz
 1.   How much work is done to transfer 0.15 C of
      charge through a potential difference of 9 V?
 2.   A voltmeter indicates that the difference in
      potential between two plates is 50 V. The
      plates are 0.02 m apart. What electric field
      intensity exists between them?
 3.   A potential difference of 0.9 V exists from
      one side to the other side of a cell membrane
      that is 5 nanometers thick. What is the
      electric field across the membrane?
Electrostatic Equilibrium


  All systems want to be at equilibrium,
   when the energy of the system is a
   minimum.
  Charges in a conductor will move until
   the electric potential is the same
   everywhere on the conductor.
Distribution of Charges on a Conductor in
Electrostatic Equilibrium

   The electric field is zero everywhere
    inside the conductor.
   Any excess charge on an isolated
    conductor will reside on its surface.
   The electric field just outside the
    conductor’s surface is perpendicular to
    the surface.
   On irregularly shaped conductors,
    charge accumulates at sharp points.
Electrical Discharges

    For an irregularly shaped conductor,
     electrical discharge is most likely to
     occur from the pointed regions since
     charge builds up there.
Millikan’s Experiment

  Robert Millikan was able to find the
   charge of an electron by suspending a
   drop of oil between two parallel plates.
  When the oil drop was suspended, the
   force of weight of the object had to be
   equal to the force exerted by the electric
   field.
Cont’d

                  Vq
             mg 
                   d
  V - potential difference between plates
   (V)
  m - mass of particle (kg)
  g - acceleration due to gravity 9.8 m/s2
  q - charge on particle (C)
  d - distance between plates (m)
     mg  Eq
 m= mass in kg
 g = acceleration due to gravity
 E = electric field intensity or strength
  (N/C)
 q = charge in Coulombs
Sample Problems - Millikan’s
Experiment
    A negatively charged oil drop weighing
     1.59*10-14 N is balanced in the electric
     field between the two oppositely charged
     plates in a Millikan apparatus. The
     difference of potential between the plates
     is 100 V and the distance between them
     is 0.0050 m. What is the field strength
     between the plates? What is the charge
     on the oil drop? How many excess
     electrons are on the drop?

				
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