Review29:008Exam 3

Ch. 12 Electrostatic Phenomena

Electric Charge

Atom is electrically neutral.

Rubbing charges objects by moving electrons from one to the other.

Charge on the electron:

Induced Charge; the ElectroscopeThe electroscope can be charged either by

• conduction (direct contact of two conductors

• or by induction.

Coulomb’s Law

Coulomb’s law:

This equation gives the magnitude of the force.

Vector addition review:

The Electric Field

The electric field is the force on a small charge, divided by the charge:

Field Lines

The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

Field Lines

Electric dipole: two equal charges, opposite in sign:

Electrostatic Potential Energy and Potential Difference

Electric potential is defined as potential energy per unit charge:

Unit of electric potential: the volt (V).

1 V = 1 J/C.

Ch. 13 Electric Circuits

Electric Current

Electric current is the rate of flow of charge through a conductor:

Unit of electric current: the ampere, A.

1 A = 1 C/s.

Electric Current

A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit!

Electric CurrentIn order for current to flow, there must be a path from one battery terminal, through the circuit, and back to the other battery terminal.

Only one of these circuits will work:

Ohm’s Law: Resistance and Resistors

Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

Ohm’s Law: Resistance and Resistors

The ratio of voltage to current is called the resistance:

Electric Power

The unit of power is the watt, W.

Electric Power

For resistors:

Resistors in Series

A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.

Resistors in Series

equivalent resistance (that single resistance that gives the same current in the circuit).

Resistors in Parallel

A parallel connection splits the current; the voltage across each resistor is the same:

19.2 Resistors in Parallel

The equivalent resistance:

Ch. 14 Magnets & Electromagnetism

Magnets and Magnetic Fields

Magnets have two ends – poles – called north and south.

Like poles repel; unlike poles attract.

Magnets and Magnetic Fields

However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

Magnets and Magnetic Fields

Magnetic fields can be visualized using magnetic field lines, which are always closed loops.

Magnets and Magnetic Fields

The Earth’s magnetic field is similar to that of a bar magnet.

Note that the Earth’s “North Pole” is really a south magnetic pole

Electric Currents Produce Magnetic Fields

an electric current produces a magnetic field.

Electric Currents Produce Magnetic Fields

The direction of the field is given by a right-hand rule.

Magnetic Field

Unit of B:

tesla, T

1 T = 1 N/A·m

Force on Electric Charge Moving in a Magnetic Field

If a charged particle is moving perpendicular to a uniform magnetic field, it experiences a force that is perpendicular to its velocity v

Right hand rule; opposite for neg charge

Force between Two Parallel Wires

If two wires carry currents I1 & I2

They experience a mutual force (per unit length of wire)

1 22 'k I IF

l r

r

Flux

Magnetic flux:

A = area of loop of wire.

Unit of magnetic flux: 1 T·m2

Induced EMF

A voltage is induced (it’s called an ‘emf’, has symbol e) when the flux through a loop of wire varies with time

Faraday’s law

[1 loop]

[N loops]

Faraday’s Law

Transformers and Transmission of Power

A transformer consists of two coils.

A changing emf in one induces an emf in the other.

The ratio of the emfs is equal to the ratio of the number of turns in each coil:

(21-6)

Transformers

This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary:

Ch. 15 Waves

Wave Motion

Wave characteristics:

• Amplitude, A

• Wavelength, λ

• Frequency f and period T

• Wave velocity (11-12)

Types of Waves: Transverse and Longitudinal

The motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal).

Types of Waves: Transverse and Longitudinal

Sound waves are longitudinal waves:

Interference

The superposition principle says that when two waves pass through the same point, the displacement is the arithmetic sum of the individual displacements.

In the figure below, (a) exhibits destructive interference and (b) exhibits constructive interference.

Interference

These figures show the sum of two waves. In (a) they add constructively; in (b) they add destructively; and in (c) they add partially destructively.

Standing Waves

Standing waves occur when both ends of a string are fixed.

There are:

• nodes, where the amplitude is always zero,

• antinodes, where the amplitude varies from zero to the maximum value.

Standing Waves

The frequencies of the standing waves on a particular string are called fundamental and harmonics.

Air Columns

A tube open at both ends (most wind instruments) has antinodes, at the ends.

Air Columns

A tube closed at one end (some organ pipes) has a node

Doppler Effect

The Doppler effect occurs when a source of sound is moving with respect to an observer.

Doppler Effect

As can be seen in the previous image:

• a source moving toward an observer has a higher frequency and shorter wavelength;

• the opposite is true when a source is moving away from an observer.

Ch. 16 Light waves & color

Electromagnetic Spectrum

Electromagnetic Spectrum

Visible light: 400 nm (violet) to 750 nm (red)

1 nm = 10-9 m

Speed of light

The wavelength and frequency of electromagnetic waves are related:

Double-Slit

If light is a wave, there should be an interference pattern.

Double-SlitThe interference occurs because each point on the screen is not the same distance from both slits.

Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).

Double-Slit

x

d

x

d

Diffraction pattern on screenhas bright fringes separated by a distance x

d

24.3 Interference – Young’s Double-Slit Experiment

Between the maxima and the minima, the interference varies smoothly.

Diffraction by a Single Slit or Disk

Light will diffract around a single slit (or around a circular obstacle).

x

d

screen

Diffraction by a Single Slit or Disk

The resulting pattern of light and dark stripes is called a diffraction pattern.

y

xy

d

Position y of the first dark fringe,

measured from the central bright spot

Interference by Thin Films