PHYSICS 212 Electricity and Magnetism

PHYSICS 212 PHYSICS 212 Electricity and Electricity and MagnetismMagnetism

1. Electric Fields1. Electric Fields

Fundamental properties of electric chargeCharging by induction and conductionCoulombs law and the electric forceElectric fieldsElectric field linesProblems / Vectors

Experiments show thatExperiments show that

Electric charge cannot be created nor destroyed #CONSERVATION OF CHARGE

Total charge of an object is always an integer multiple of a basic charge “e”#CHARGE QUANTIZATION

Charge Conservation

Two types of charge #Named + and -#Like charges repel #Unlike charges attract

Repulsion and attraction are

FORCES

Types of Charge

Forces on Charges

Coulombs LawThe force between charges is given byCOULOMBS LAW

F k 2Q1Q

2rˆ r

Meaning of Symbols

Coulombs constant

Unit vector pointing from charge 1 to

charge 2

The distance between the charges

The force exerted on charge 2 by charge 1

k 9

9 102Nm

2C

r

r

F

Atoms = #Nucleus

is very small less than 10-15 m in diameter, but heavy Contains protons and neutrons

plus #Electrons

Diameter approx. 10-10 mare very light but make up the volume of the atom

Atomic Structure

MaterialsMaterials are atoms bound together by electronsElectrons are on the outside

#Produce the quality of

“Solidness”

Different materials hold their electrons with different forcesRubbing one material on the other displaces electronsone material becomes positive the other negative

Charging by Induction

Charging by induction

Charging by ConductionCharging by conduction

+ + + + + ++ + + + + +- - - + + + - - - + + +

+ - + + + + - + - + + +

+ - + + - + + - +

++

F k 2Q1Q

2rˆ r

Coulombs Law

Force due to Many Sources

at a point r The electric Force due to many point charge sources on a charge q

is the vector sum of all forces due to source charges

Diagram of Many SourcesF

r

F1

F2

F3

Q1

Q2

Q3

q

F r iF

i r

Vector Sum

Force Due to Continuous Source

The Electric Force due to a continuous distribution of point charge sources: #A charged solid

at a point r on a charge qis the vector integral of all forces due to the source charges

Diagram of Continuous Source

r dFQ

F

q

F(r) dF(r)solid

Vector Integral

The Electric Field is the

Force per unit charge

The Electric Field is the

Force per unit charge

Electric Field

Q1E ˆ r F Q2

E ˆ r kQ1

2rˆ r

Mathematical Expression

at a point r The Electric Field Electric Field due to many point charge sources is the vector sum of all fields due to source charges

Meaning of Symbols

E1

E2

E3 r

E Q1

Q2

Q3

Diagram of Field due to Point Sources

E r iEi r

Vector Sum of Fields

Diagram of Field Due to Continuous Source

r dEQ

E

E(r) dE(r)solid

Vector Integral

Electric FieldElectric Field lines are lines that have

Electric Field vectors as tangent lines at each point.

Electric Field Lines

Picture of Field Lines

Picture of Field Lines

Picture of Field Lines

Picture of Field Lines