Electrostatics Electric Charges and Fields. Static Electricity u Called static because charge not...
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Transcript of Electrostatics Electric Charges and Fields. Static Electricity u Called static because charge not...
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 coulombs
r = distance between charges
k = 8.99 x 109 Nm2/C2 (Coulomb’s constant)
1 22E
Q QF k
r
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:
0q
FE
2r
kQE
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
dF
q
WV
q
FE
d
VE
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
d
kQd
d
kQEdV
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
d
AC 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 2
QPE CV QV
C
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 . . .