CHAPTER 1717.1 Electric forces17.2 Coulombs Law17.3 Electric field17.5 Electric flux and Gauss’s Law

CHAPTER 1818.1 Electric potential energy18.2 Electric potential voltage18.3 Equipotential lines, surfaces18.4 Capacitors18.5 Dielectrics18.6 Electricity and the Atmosphere18.7 Biological examples18.8 Where is the energy located? 

Chapter 1919.1 Electric current19.2 Batteries19.3 Current & Voltage in a Resistor  19.4 Direct Current Circuits19.6 Ammeters & Voltmeters19.8 Currents in human body

CHAPTER 2020.1 Sources of Magnetic Fields20.2 Magnetic Forces & Bar Magnets20.3 Magnetic Force on moving charge20.4 Magnetic force on Electric Current20.5 Torque and current loops20.6 Motion on Q, M in E & B Fields20.7 Ampere’s Law20.8 Magnetic materials

EXAM 1 SUMMARY

Figure 17‐2 p546

CHAPTER 17

Figure 17‐3 p547

Figure 17‐11 p554

ELECTRIC FIELD

Figure 17‐12 p554

ELECTRIC FIELD LINES

Figure 17‐16b p557

VECTOR ADDITION OF ELECTRIC FIELD AT A

Figure 17‐27a p563

ELECTRIC FLUX ΦE

UNIFORM

Figure 17‐27c p563

Figure 17‐27 p563

Gauss’ Law• Gauss’ Law says that the electric flux

through any closed surface is proportional to the charge q inside the surface

• The constant εo is the emissitivity of free space– This was encountered in one form of Coulomb’s

Law• Since the flux depends on the electric field,

Gauss’ Law can be used to find the field

Section 17.5

Eo

q

Gauss’ Law: Point Charge

• Choose a Gaussian surface– Want a surface that

will make the calculation as easy as possible

– Choose a surface that matches the symmetry of the problem

• For a point charge, the field lines have a spherical symmetry

Section 17.5

GAUSS’S LAW

ΦE= q / ε0

Point charge Example

ΦE= 4πr2 E = q / ε0

E = q / 4πr2ε0 

Figure 18‐1 p584

CHAPTER 18

WORK AND POTENTIAL ENERGY

Figure 18‐9 p591

Figure 18‐18 p599

Figure 18‐21 p600

Figure 18‐16 p598

p614

Figure 18‐22b p600

Figure 18‐26 p605

p615

Cequiv =C1+C2

1/Cequiv= 1/C1 + 1/C2

Figure 18‐23b p601

ΔV = Ed

Figure 20‐11b p673

FORCE ON ELECTRIC DIPOLE

Figure 20‐2b p669

Figure 18‐31 p607

Figure 18‐31c p607

Qd reduces the Electric Field produced by Qby a factor κ, the dielectric constant

V = E/κ  d To restore E to air dielectric value  |Q| must beincreased to (1+κ ) |Q|  Thus C increases to κ CO  where  CO = εO A/d

The Energy Stored in the Capacitor is the electrostatic energy density ½ εO E2 times the volume of the parallel plate capacitor Ad

WHERE IS THE ENERGY STORED?

Figure 19‐1c p624

CHAPTER 19

Figure 19‐2 p625

Figure 19‐8 p630

ρ the resistivity of the material

RESISTOR

Figure 19‐3 p625

Figure 19‐4c p626

Figure 19‐14 p637

Figure 19‐17b p638

Figure 19‐20 p641

Kirchhoff’s Loop Rule

• Consider the electric potential energy of a test charge moving through the circuit

• ∆V = ε – I R = 0– For the entire circuit– Assumes wires have no resistance

Section 19.4

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Energy Dissipated in a Resistor

• The test charge gained energy when it passed through the battery

• It lost energy as it passed through the resistor

• The energy is converted into heat energy inside the resistor– The energy is dissipated as heat– It shows up as a temperature increase of the

resistor and its surroundings

Section 19.4

Power

• In the resistor, the energy decreases by qV = (I ∆t) V– Power is energy / ∆t P = I V

• Applying Ohm’s Law, P = I² R = V² / R• The circuit converts chemical energy from

the battery to heat energy in the resistors– Applies to all circuit elements

Section 19.4

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EQUIVALENT RESISTOR AND CAPACITANCE RELATIONSHIPS

Figure 19‐38 p652

Table 19‐3 p655

MAGNET FIELDS

• A bar magnet is a permanent magnet in the shape of a bar

• The symbol for the magnetic field is

• The magnetic field lines can be deduced from the pattern of the iron filings– The filings are small,

needle-shaped, permanent magnets

Section 20.1

B

CHAPTER 20

Magnetic Field Lines• The magnetic poles are

indicated at the ends of the bar magnet– Called north and south

• The magnetic poles are analogous to positive and negative charges

• The north poles of the filings are attracted to the south pole of the bar magnet

Section 20.1

Figure 20‐2a p669

Magnetic Forces & Bar Magnets• To determine the total

force on the bar magnet, you must look at the forces on each pole

• The total force is zero• The total torque is

non-zero• The torque acts to

align the bar magnet along the magnetic field

Section 20.2

Force on Moving Charge• Magnetic force acts on individual charges• The force depends on the velocity of the charge

– If the charge is not moving, there is no magnetic force• If a positive charge, q, is moving with a given

velocity in an external magnetic field, then the magnitude of the force on the charge is

– FB = q v B sin θ

– The angle θ is the angle between the velocity and the field

Section 20.3

Right Hand Rule Number 2• To determine the

direction of the force, use right hand rule number 2

• Point the figures of your right hand in the direction of the velocity and wrap them in the direction of the field

• Your thumb points in the direction of the force

Section 20.3

Figure 20‐15 p676

MAGNETIC  FORCE ON A CURRENT 

FB

|FB| = |BIL cos θBV |

Magnetic Field from Current

• Moving charges produce magnetic fields– An electric current consists of moving charges, so it

will produce a magnetic field• The iron filings show the magnetic field pattern

due to the current

Section 20.1

Figure 20‐9b p672

MAGNETIC FIELD FROM A CURRENT LOOP

Figure 20‐5b p670

Figure 20‐16a p677

Figure 20‐16b p677

Figure 20‐24 p682

Figure 20‐24a p682

τ = N I L2 sinθ .  For Area  A of  Loopthen    τ = N I A B sinθ

Motion in Two Fields

• The motion of an electric charge in the presence of both an electric field and a magnetic field is of general interest.

• Two applications include– Mass spectrometer– Hall Effect

Section 20.6

Mass Spectrometer• Allows for the

separation of ions according to their mass or charge

• The ions enter with some speed v

• They pass into a region where the magnetic field is perpendicular to the velocity

Section 20.6

Hall Effect• An electric current is

produced by moving electric charges

• A particular value of current can be produced by positive charges moving to the right or negative charges to the left

• The Hall Effect can distinguish between the two options

Section 20.6

Hall Effect, final• With negative charge

carriers, an excess negative charge accumulates on the top edge

• Measuring the potential difference distinguishes between positive or negative charge carriers producing the current

Section 20.6

Ampère’s Law

• There are two ways to calculate the magnetic field produced by a current– One way treats each small piece of wire as a

separate source• Similar to using Coulomb’s Law for an electric field• Mathematically complicated

– Second way is to use Ampère’s Law• Most useful when the field lines have high

symmetry• Similar to using Gauss’s Law for an electric field

Section 20.7

Ampère’s Law, cont.• Relates the magnetic

field along a path to the electric current enclosed by the path

• For the path shown, Ampère’s Law states that

– μo is the permeability of free space

– μo = 4 π x 10-7 T . m / A

o enclosedclosedpath

B L I

Section 20.7

Field from a Current Loop• It is not possible to

find a path along which the magnetic field is constant– So Ampère’s Law

cannot be easily applied

• From other techniques, the field at the center of the loop is o IB

R

2

Section 20.7

Field Inside a Solenoid

• By stacking many loops close together, the field along the axis is much larger than for a single loop

• A helical winding of wire is called a solenoid– More practical than stacking single loops Section 20.7

Solenoid, final

• The uniform magnetic field inside the solenoid is given by

– For a solenoid with a length much greater than the diameter

osolenoid

N IBL

Section 20.7

Motion of Electrons• The motion of an electron around a nucleus can

be pictured as a tiny current loop– The radius is approximately the radius of the atom– The direction of the resulting magnetic field is

determined by the orientation of the current loop• Using right-hand rule 1

Section 20.8

Electron Spin• The electron also

produces a magnetic field due to an effect called electron spin

• The spinning charge acts as a circulating electric current

• The electron has a spin magnetic moment

Section 20.8

Magnetic Field in an Atom

• The correct explanation of electron spin requires quantum mechanics

• Confirms an atom can produce a magnetic field in two ways– Through the electron’s orbital current loop– Through the electron’s spin

• The total magnetic field produced by a single atom is the sum of these two fields

Section 20.8

Figure 20‐37 p692