Electrostatics Electric Charges and Fields
Feb 25, 2016
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
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.
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
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
Coulomb’s Law Realized by many early experimenters, 1785
Coulomb first to quantify with correct constant Coulomb’s Law:
Q = charge in coulombsr = distance between chargesk = 8.99 x 109 Nm2/C2 (Coulomb’s constant)
1 22E
Q QF kr
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.
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 Fields Then electric field strength in
newtons/coulomb For a point charge, substituting the force
from Coulomb’s law, the equation becomes:
0qFE
2rkQE
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
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 charge
Since then also q
dFq
WV
qFE
dVE
Electric Potential For a point charge (or spherical charge
distribution , which can be treated as a point charge)
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
dkQd
dkQEdV 2
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
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 F 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,
for vacuum = 1, about the same for air Capacitance increases by factor of 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 10-12 F/m
dAC 0
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
221 1
2 2 2QPE CV QVC
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 equation1/Ceq= 1/C1+1/C2+1/C3 . . .