Electrostatics by ewghwehws


    Electric Charges and Fields
Static Electricity
    Called static because charge not pushed by
     battery, generator, or other emf source
    Early experimenters found two types of
     charge, positive and negative
    Ben Franklin (1750’s) made decision which
     type would be called neg. and pos.
    Discovery of electron (Thomson, 1897)
     showed mobile charge is usually negative
Electric Charges
   Enormous    amounts of charge exist in all
    matter but usually no effects are seen due to
    equal number of positive and negative
   Electrification occurs when charges are
   Electric charge is conserved—no charge is
    created or destroyed, just rearranged
Electric charges
   Electrons  carry negative charge, protons
    carry positive charge
   Excess electrons makes a negative charge;
    lack of electrons makes a positive charge
   Use electroscope to detect static charge
Measuring Electric Charge
   Unit of charge is the coulomb (C), very
    large amount of charge, equal to 6.25 x 1018
   The symbol for charge in an equation is q
    or Q
   Electric charge is quantized—the amount of
    charge is always a multiple of a very small
Measuring Electric Charge
   Thomson   measured the ratio of charge to
    mass for an electron, but was unable to
    measure either quantity separately
   Robert Millikan (1909), with famous oil
    drop experiment, discovered basic unit of
    charge: e = 1.60 x 10-19 C
   Electrons and protons each have an amount
    of charge equal to e
Thomson’s Cathode Ray Tube
Millikan’s Experiment
J. J. Thomson
                Robert Millikan (1868 -
Electrical Forces
   Electrical   charges exert forces on each
   Law of electrostatics: Like charges repel;
    opposites attract
 Conductor:   readily transmits electric charge
 Insulator: inhibits transfer of charge
 Metals are good conductors because of cloud
  of free electrons surrounding crystal lattice
 Electrons tightly bound in insulators
 Excess charge placed on insulator stays put in
  one area; in metals, charge spreads evenly
Charge Transfer
 Induction:  charged object brought close, but
  not touching, causes charge separation
  (polarization) in electroscope (or other object)
 Transfer by induction: if connection to ground
  (infinite charge source or sink) provided while
  charge is near (so electrons can travel on or
  off), residual charge of opposite type will
  remain on electroscope
Charging by Induction:

                     Grounding allows
                     charges to move off
                     sphere leaving opposite
                     residual charge.
Charging by Induction: Two
                  Aftercharging rod is
                   removed, spheres
                   have opposite
Charge Transfer
   Conduction:   electrical contact is made
   Charging an electroscope by conduction:
    Charged object brought in contact with
    electroscope, some of excess charge
    transferred leaving residual charge of same
    type on electroscope
 All matter contains huge amounts of + and - charge
 Charges can be separated, transferred by contact
 Electric charge is conserved and quantized
 Like charges repel; opposite charges attract
 Conductors have free electrons; insulators inhibit charge
  flow, electrons bound
 Electroscope detects charge state; charged by induction
  or conduction.
Forces Between Charges
   Force  between charges obeys law very
    similar to law of gravitation
   For spherical charge distributions, force
    acts like all charge concentrated at center
   Can be attractive (-) or repulsive (+) force
   Force directly proportional to product of
    two charges, inversely prop. to square of
    distance between charges
Charles Augustin de Coulomb

  1736 - 1806
Coulomb’s Law
         by many early experimenters, 1785
 Realized
  Coulomb first to quantify with correct constant
 Coulomb’s Law:                    Q1Q2
                               FE  k    2
  Q = charge in coulombs                r
  r = distance between charges
  k = 8.99 x 109 Nm2/C2 (Coulomb’s constant)
Electrical Forces
   Electrical forces are equal and opposite
    interactions between two charged objects
   Like all forces, measured in newtons
   If more than two charges are present, forces
    between each pair of charges are calculated,
    then vector sum must be found for total
    force on each charge.
Electrical Forces with Three
Electric Fields
    Proposed   by Michael Faraday (1832) to
     illustrate how forces can act with no contact
    Draw lines of force that start at pos. charges
     and end on neg. charges
    Number of lines in area represent strength
     of field (magnitude)
Electric Fields
    Field lines end in arrows like vectors
    Arrowheads point towards neg. charge;
     show direction of force on pos. test charge
    Strength of field around a charge, Q, is
     calculated by using pos. test charge qo (real
     or imaginary), small enough to be
Electric Field: Isolated Charges
 Electric Field: Like Charges

Two Opposite Charges
Electric Fields
    Then  electric field strength E  F
     in newtons/coulomb                    q0
    For a point charge, substituting the force
     from Coulomb’s law, the equation
                 E 2
   Forces  between charges is calculated using
    Coulomb’s Law, an inverse square law
   Electric field is visualized by field lines
    showing magnitude and direction of force
    on positive test charge
   Field strength expressed in newtons of
    force per coulomb of charge
    Electric Potential
Electric Potential Energy
  A   charge in an electric field has potential
    energy and ability to do work due to
    electrostatic force
   Potential energy equals the work done to
    bring a charge from an infinite distance to
    its current position in the field
   Electric potential energy depends on the
    amount of charge present
Electric Potential
    Electricpotential equals electric potential
     energy divided by amount of charge present
    Potential is independent of amount of
     charge present (if any)
    Measured in volts (V); 1 V = 1 J/ 1 C;
     symbol also V
    Referenced with respect to a standard,
     usually V = 0 volts at infinite distance
Electric Potential
    Potential  difference between two points in
     electric field = work done moving charge
     between two points divided by amount of
     charge               W F d
                   V        
                         q       q
    Since             then also
                F                       V
             E                      E
                q                       d
Electric Potential
    For  a point charge (or spherical charge
     distribution , which can be treated as a point
     charge)               kQ      kQ
                V  Ed  2 d 
                           d        d
    The electric field strength can be expressed
     in N/C or in V/m
    Any point in field can be described in terms
     of potential whether charge is present or not
 Earth is considered an infinite source or sink
  for charge - will absorb or give up electrons
  without changing its overall charge
 Earth’s potential considered to be zero
 Any object connected to earth is said to be
  “grounded” (earthed in England)
 All building circuitry has wire connected to
  stake in ground
Charge on a Conductor
   All  excess charge on conductor resides on
    its outside surface
   At all points inside a conductor the electric
    field is zero
   All points of conductor (or connected by
    conducting wires) are at same potential
   Surrounding area with a conductor shields
    from external fields
Distribution of Charge
   Ifconductor is sphere, charge density will
    be uniform over surface
   For other shapes, charge density varies,
    more concentrated around points, corners
Distribution of Charge
   Spark discharges occur from points: air
    molecules become ionized into plasma
   Lightning is static spark discharge -
    millions of volts potential
   Lightning rods create points for spark
    discharge directing charge to ground - Ben
    Franklin’s invention
Equipotential Surfaces
   Real  or imaginary surface surrounding a
    charge having all points at same potential
   In two dimensions, equipotential lines
   Equipotential surface always perpendicular
    to field lines
   Point charge has spherical equipotential
    Capacitors and Capacitance
  Electricaldevice for storing charge
  Consists of two conducting surfaces (plates)
   separated by air or insulator (dielectric)
  Amount of charge that can be stored depends
   on geometry of capacitor-area of plates and
   distance between them-and type of dielectric
  Early capacitor called Leyden jar
   The ability to store charge
   Measured in farads (F) named for Faraday
    1farad = 1 coulomb/1 volt
   Capacitance = stored charge / potential
    between plates C = q/V
   Farad very large amount of capacitance;
    most capacitors measured in mF or pF
   Insulating material between capacitor plates
   Increase amount of charge that can be
    stored by a factor of the material’s
    dielectric constant, k
   k for vacuum = 1, about the same for air
   Capacitance increases by factor of k also
  For charged cap. not connected to battery,
   dielectric will reduce potential between plates
  Molecules in dielectric become aligned with
   electric field between plates
  This sets up opposing electric field that
   weakens electric field between plates
  Dielectric can be polar or non-polar
Parallel Plate Capacitors
   Capacitance  is directly proportional to
    plate area and inversely proportional to
    distance between plates
   Capacitance is increased by dielectric
   Proportionality constant is ε0, the
    permittivity of free space: ε0 = 8.85 x
    10-12 F/m                 A
                  C   0k
Stored Energy
   Work   done moving charge onto plates
    during charging process is stored as energy
    in the electric field between the plates
   Energy can be used at a later time to do
    work on charges, moving them as capacitor
           PE  CV  QV 
                      2   1
Combinations of Capacitors
   Caps  can be connected in two ways,
    parallel or series
   circuit symbol for capacitor is
   Series connection
   Parallel connection
Combinations of Capacitors
   For  caps in parallel, equivalent capacitance
    of combination is sum of separate
    capacitances; CT = C1 + C2 + C3 . . .
   all caps have same potential difference
    across them: V1 = V2 = V3 . . .
   For series connection, equivalent
    capacitance is found with equation
    1/Ceq= 1/C1+1/C2+1/C3 . . .
Combinations of Capacitors
   In  series, eq. capacitance always smaller
    than smallest capacitor in series
   Caps in series all have same charge:
    q 1 = q 2 = q3 . . .
   Total potential difference across series of
    caps is sum of potential difference across
    each cap.: VT = V1 + V2 + V3 . . .

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