Electrostatics

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
Enormous amounts of charge exist in all matter but usually neutral; electrification occurs when charges are separated
Excess electrons makes negative charge; lack of electrons makes positive charge
Use electroscope to detect static charge
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

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
Conduction: electrical contact is made
Charging by conduction: Charged object brought in contact with electroscope, some of excess charge transferred leaving residual charge of same type on electroscope

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

Realized by many early experimenters, in 1785 Coulomb was first to quantify with correct constant
Coulomb's Law: F = kQ₁Q₂/d²
Q = charge in coulombs; d = distance between charges in meters
Unit of charge is coulomb (C), very large amount of charge
k = 8.987 x 10⁹ Nm²/C²: Coulomb's constant

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)
Field lines end in arrows like vectors
Arrowheads point towards neg. charge; show direction of force on pos. test charge
Strength of field is calculated by using pos. test charge q (real or imaginary), small enough to be negligible
Then electric field strength E = F/Q whose units are newtons/coulomb

Charge in electric field has potential energy and ability to do work due to electrostatic force
Potential energy magnitude equals work done to bring charge from infinite distance to position in field
Electric potential energy depends on amount of charge present

Electric potential energy divided by amount of charge present
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
Potential difference between two points in electric field = work done moving charge between two points divided by amount of charge V = W/q
Now can describe electric field strength in volts/meter
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

All excess charge on conductor resides on its surface
All points of conductor (or connected by conducting wires) are at same potential
If conductor is sphere, charge density will be uniform over surface
For other shapes, charge density varies, more concentrated around points, corners
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

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

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 dielcetric
Early capacitor called Leyden jar

Insulating material between capacitor plates
Increases amount of charge that can be stored by a factor of the material's dielectric constant, κ
κ for vacuum = 1, about the same for air
Capacitance increases by factor of κ 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

Caps can be connected in two ways, parallel or series
Circuit symbol for capacitor is two parallel lines of equal length or one straight line and one curved line
Series connection (draw)
Parallel connection (draw)
For caps in parallel, equivalent capacitance of combination is sum of separate capacitances
C_T = C₁ + C₂ + C₃ . . .
all caps have same potential difference across them: V₁ = V₂= V₃ . . .
For series connection, equivalent capacitance is found with equation
1/C_eq= 1/C₁+1/C₂+1/C₃ . . .
In series, eq. capacitance always smaller than smallest capacitor in series
Caps in series all have same charge
q₁ = q₂= q₃ . . .
Total potential difference across series of caps is sum of potential difference across each cap.: V_T = V₁ + V₂ + V₃ . . .

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