Download Electrostatics

Electrostatics
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
charges
 Electrification occurs when charges are
separated
 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
electrons
 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
amount
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 1953
Electrical Forces
 Electrical
charges exert forces on each
other
 Law of electrostatics: Like charges repel;
opposites attract
Conduction
 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
Grounding allows
charges to move off
sphere leaving opposite
residual charge.
Charging by Induction: Two
spheres
 After
charging rod is
removed, spheres
have opposite
charges
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
Electroscope
Summary
 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
 Realized
by many early experimenters, 1785
Coulomb first to quantify with correct constant
Q1Q2
 Coulomb’s Law:
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
Charges
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
negligible
Electric Field: Isolated Charges
Electric Field: Like Charges
Positive
charges
Two Opposite Charges
Electric Fields


electric field strength E  F
in newtons/coulomb
q0
 For a point charge, substituting the force
from Coulomb’s law, the equation
becomes:
 Then
kQ
E 2
r
Summary
 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
Electrostatics
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
 Electric
potential 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
W F d
charge
V
 Since
F
E
q
q

q
then also
V
E
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
Grounding
 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
 If
conductor 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
surfaces
Electrostatics
Capacitors and Capacitance
Capacitor
 Electrical
device 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
Capacitance
 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
Dielectric
 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
Dielectric
 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
constant
 Proportionality constant is ε0, the
permittivity of free space: ε0 = 8.85 x
A
10-12 F/m
C   0k
d
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
discharges
2
Q
PE  CV  QV 
2C
1
2
2
1
2
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 . . .