Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18.

Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18

Fig. 15-CO, p.497

First Observations – Greeks Observed electric and magnetic

phenomena as early as 700 BC Found that amber, when rubbed,

became electrified and attracted pieces of straw or feathers

Also discovered magnetic forces by observing magnetite attracting iron

Fig. 15-1b, p.498

Fig. 15-2, p.499

Fig. 15-3a, p.499

Fig. 15-1, p.498

Properties of Charge, final Charge is quantized

All charge is a multiple of a fundamental unit of charge, symbolized by e

Quarks are the exception Electrons have a charge of –e Protons have a charge of +e The SI unit of charge is the Coulomb (C)

e = 1.6 x 10-19 C

Conductors Conductors are materials in which

the electric charges move freely in response to an electric force Copper, aluminum and silver are good

conductors When a conductor is charged in a

small region, the charge readily distributes itself over the entire surface of the material

Insulators Insulators are materials in which

electric charges do not move freely Glass and rubber are examples of

insulators When insulators are charged by

rubbing, only the rubbed area becomes charged

There is no tendency for the charge to move into other regions of the material

Semiconductors The characteristics of

semiconductors are between those of insulators and conductors

Silicon and germanium are examples of semiconductors

Charging by Conduction A charged object (the rod)

is placed in contact with another object (the sphere)

Some electrons on the rod can move to the sphere

When the rod is removed, the sphere is left with a charge

The object being charged is always left with a charge having the same sign as the object doing the charging

Fig. 15-5a, p.501

Fig. 15-5b, p.501

Coulomb’s Law Coulomb shows that an electrical force

has the following properties: It is along the line joining the two particles

and inversely proportional to the square of the separation distance, r, between them

It is proportional to the product of the magnitudes of the charges, |q1|and |q2|on the two particles

It is attractive if the charges are of opposite signs and repulsive if the charges have the same signs

Coulomb’s Law, cont. Mathematically,

ke is called the Coulomb Constant ke = 8.9875 x 109 N m2/C2

Typical charges can be in the µC range Remember, Coulombs must be used in the

equation Remember that force is a vector quantity Applies only to point charges

Coulomb's law

2

21e r

qqkF

Characteristics of Particles

Fig. 15-6a, p.502

Fig. 15-6b, p.502

Electrical Forces are Field Forces This is the second example of a field

force Gravity was the first

Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them

There are some important similarities and differences between electrical and gravitational forces

The Superposition Principle The resultant force on any one

charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as

vectors

Fig. 15-8, p.504

Electrical Forces are Field Forces This is the second example of a field

force Gravity was the first

Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them

There are some important similarities and differences between electrical and gravitational forces

Electrical Force Compared to Gravitational Force Both are inverse square laws The mathematical form of both laws is

the same Masses replaced by charges

Electrical forces can be either attractive or repulsive

Gravitational forces are always attractive Electrostatic force is stronger than the

gravitational force

The Superposition Principle The resultant force on any one

charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as

vectors

Fig. 15-8, p.504

Superposition Principle Example

The force exerted by q1 on q3 is

The force exerted by q2 on q3 is

The total force exerted on q3 is the vector sum of

and

13F

13F

23F

23F

Fig. 15-9, p.505

Electric Field

Mathematically,

SI units are N / C Use this for the magnitude of the field The electric field is a vector quantity The direction of the field is defined to be

the direction of the electric force that would be exerted on a small positive test charge placed at that point

2e

o

k Qq r

F

E

Direction of Electric Field The electric field

produced by a negative charge is directed toward the charge A positive test

charge would be attracted to the negative source charge

Electric Field Lines A convenient aid for visualizing

electric field patterns is to draw lines pointing in the direction of the field vector at any point

These are called electric field lines and were introduced by Michael Faraday

Fig. 15-13a, p.510

Fig. 15-13b, p.510

Electric Field Line Patterns An electric dipole

consists of two equal and opposite charges

The high density of lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns Two equal but like point

charges At a great distance from

the charges, the field would be approximately that of a single charge of 2q

The bulging out of the field lines between the charges indicates the repulsion between the charges

The low field lines between the charges indicates a weak field in this region

Electric Field Patterns Unequal and

unlike charges Note that two

lines leave the +2q charge for each line that terminates on -q

Fig. 15-18a, p.513

Fig. 15-18b, p.513

Van de GraaffGenerator An electrostatic generator

designed and built by Robert J. Van de Graaff in 1929

Charge is transferred to the dome by means of a rotating belt

Eventually an electrostatic discharge takes place

Electrical Potential Energy of Two Charges

V1 is the electric potential due to q1 at some point P

The work required to bring q2 from infinity to P without acceleration is q2V1

This work is equal to the potential energy of the two particle system

r

qqkVqPE 21e12

The Electron Volt The electron volt (eV) is defined as the

energy that an electron gains when accelerated through a potential difference of 1 V Electrons in normal atoms have energies of

10’s of eV Excited electrons have energies of 1000’s of

eV High energy gamma rays have energies of

millions of eV 1 eV = 1.6 x 10-19 J

Equipotential Surfaces An equipotential surface is a

surface on which all points are at the same potential No work is required to move a charge

at a constant speed on an equipotential surface

The electric field at every point on an equipotential surface is perpendicular to the surface

Equipotentials and Electric Fields Lines – Positive Charge

The equipotentials for a point charge are a family of spheres centered on the point charge

The field lines are perpendicular to the electric potential at all points

Equipotentials and Electric Fields Lines – Dipole Equipotential lines

are shown in blue Electric field lines

are shown in red The field lines are

perpendicular to the equipotential lines at all points

Capacitance, cont

Units: Farad (F) 1 F = 1 C / V A Farad is very large

Often will see µF or pF

V

QC

Parallel-Plate Capacitor The capacitance of a device

depends on the geometric arrangement of the conductors

For a parallel-plate capacitor whose plates are separated by air:

d

AC o

Parallel-Plate Capacitor, Example

The capacitor consists of two parallel plates

Each have area A They are separated by a

distance d The plates carry equal and

opposite charges When connected to the

battery, charge is pulled off one plate and transferred to the other plate

The transfer stops when Vcap = Vbattery

Demo 2

Capacitors in Parallel The total charge is

equal to the sum of the charges on the capacitors

Qtotal = Q1 + Q2

The potential difference across the capacitors is the same

And each is equal to the voltage of the battery

Fig. 16-19, p.551

Fig. 16-20, p.552

Fig. P16-34, p.564

Fig. 16-21, p.553

Energy Stored in a Capacitor Energy stored = ½ Q ΔV From the definition of capacitance,

this can be rewritten in different forms

C2

QVC

2

1VQ

2

1Energy

22

Dielectric Strength For any given plate separation,

there is a maximum electric field that can be produced in the dielectric before it breaks down and begins to conduct

This maximum electric field is called the dielectric strength

Table 16-1, p.557

Electric Current Whenever electric charges of like signs

move, an electric current is said to exist The current is the rate at which the

charge flows through this surface Look at the charges flowing perpendicularly

to a surface of area A

The SI unit of current is Ampere (A) 1 A = 1 C/s

QI

t

Electric Current, cont The direction of the current is the

direction positive charge would flow This is known as conventional current

direction In a common conductor, such as copper, the

current is due to the motion of the negatively charged electrons

It is common to refer to a moving charge as a mobile charge carrier A charge carrier can be positive or negative

Current and Drift Speed

Charged particles move through a conductor of cross-sectional area A

n is the number of charge carriers per unit volume

n A Δx is the total number of charge carriers

Current and Drift Speed, cont The total charge is the number of

carriers times the charge per carrier, q ΔQ = (n A Δx) q

The drift speed, vd, is the speed at which the carriers move vd = Δx/ Δt

Rewritten: ΔQ = (n A vd Δt) q Finally, current, I = ΔQ/Δt = nqvdA

Current and Drift Speed, final If the conductor is isolated, the

electrons undergo random motion When an electric field is set up in

the conductor, it creates an electric force on the electrons and hence a current

Charge Carrier Motion in a Conductor

The zig-zag black line represents the motion of charge carrier in a conductor

The net drift speed is small

The sharp changes in direction are due to collisions

The net motion of electrons is opposite the direction of the electric field Demo

p.578

Resistance In a conductor, the voltage applied

across the ends of the conductor is proportional to the current through the conductor

The constant of proportionality is the resistance of the conductor

VR

I

Fig. 17-CO, p.568

Resistance, cont Units of resistance are ohms (Ω)

1 Ω = 1 V / A Resistance in a circuit arises due to

collisions between the electrons carrying the current with the fixed atoms inside the conductor

Ohm’s Law Experiments show that for many materials,

including most metals, the resistance remains constant over a wide range of applied voltages or currents

This statement has become known as Ohm’s Law ΔV = I R

Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be

ohmic

Resistivity The resistance of an ohmic conductor is

proportional to its length, L, and inversely proportional to its cross-sectional area, A

ρ is the constant of proportionality and is called the resistivity of the material

LR

A

Table 17-1, p.576

Temperature Variation of Resistivity For most metals, resistivity

increases with increasing temperature With a higher temperature, the

metal’s constituent atoms vibrate with increasing amplitude

The electrons find it more difficult to pass through the atoms

Temperature Variation of Resistivity, cont For most metals, resistivity increases

approximately linearly with temperature over a limited temperature range

ρ is the resistivity at some temperature T ρo is the resistivity at some reference

temperature To To is usually taken to be 20° C = 68 ° F is the temperature coefficient of resistivity

)]TT(1[ oo

Temperature Variation of Resistance Since the resistance of a conductor

with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance

)]TT(1[RR oo

Electrical Energy and Power, cont The rate at which the energy is lost

is the power

From Ohm’s Law, alternate forms of power are

QV I V

t

22 V

I RR

Electrical Energy and Power, final The SI unit of power is Watt (W)

I must be in Amperes, R in ohms and V in Volts

The unit of energy used by electric companies is the kilowatt-hour This is defined in terms of the unit of

power and the amount of time it is supplied

1 kWh = 3.60 x 106 J

Fig. Q18-13, p.616

More About the Junction Rule I1 = I2 + I3 From

Conservation of Charge

Diagram b shows a mechanical analog

RC Circuits A direct current circuit may contain

capacitors and resistors, the current will vary with time

When the circuit is completed, the capacitor starts to charge

The capacitor continues to charge until it reaches its maximum charge (Q = Cε)

Once the capacitor is fully charged, the current in the circuit is zero

Charging Capacitor in an RC Circuit

The charge on the capacitor varies with time

q = Q(1 – e-t/RC) The time constant,

=RC The time constant

represents the time required for the charge to increase from zero to 63.2% of its maximum

Notes on Time Constant In a circuit with a large time

constant, the capacitor charges very slowly

The capacitor charges very quickly if there is a small time constant

After t = 10 , the capacitor is over 99.99% charged

Household Circuits The utility company

distributes electric power to individual houses with a pair of wires

Electrical devices in the house are connected in parallel with those wires

The potential difference between the wires is about 120V

Effects of Various Currents 5 mA or less

Can cause a sensation of shock Generally little or no damage

10 mA Hand muscles contract May be unable to let go a of live wire

100 mA If passes through the body for just a few

seconds, can be fatal