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

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.

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

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

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 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

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 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 . . .

Combinations of Capacitors

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.: VT = V1 + V2 + V3 . . .