ELECTROSTATICS

2 TYPES: positive (e.g. glass rod rubbed with silk) and negative (e.g. rubber rod rubbed withfur)Law governing charges:a. two charges of same electrification repel; while unlike charges attractb. charge is conserved in an isolated system

Unit of Charge: in multiples ofe = 1.6 x 10-19 coulomb

Conductors, Insulators, SemiconductorsConductors – capacity to allow motion of chargesInsulators- passive substances as far as charge motion is concernedSemiconductors – substances which attain conductive abilities in the presence of

impurities and variations in temperature

Coulomb’s law: the electrostatic force between two charged objects varies as the inverse square of thedistance between them F = k qq’/r2

k = 9 x 109 nt – m2/coul2

q q’

r

Con’t

k = 1/4 o

o = permittivity of free space

= 8.8542 x 10-19

coul2

/nt-m2

A field of force or electric field intensity is set up inthe vicinity of a charged body.

E = F/q’ = k q/ r2

where F is the force exerted by charge q on q’Hence F = Eq’ is the force experienced by q’ in an electric field

Electric field

Principle of Superposition: the total electric force on a particular charge q due to a number of other charges is just the vector sum of all the individual forces, i. e.

F (net) = F i i = 1, 2, …, n

Gauss’ law: the net flux (or number of lines of force) coming from a closed surface is always equal to the total quantity of charge contained in the surface

E = [1/oAo] qi i = 1, 2, …, n

where o= permittivity of free space Ao = total area of closed surface

Electric Potential

The potential energy of a charge q a distance r froma source charge Q isU = k qQ/r

The electric potential V is just U/Q in joules/coulomb V = U/Q is the electric potential at any point in the electric field

V obeys the principle of superposition, that is,

V(net) = V i i = 1, 2, …, n

Potential difference: V = U/Q in joules/coulomb or volt

Capacitance C

-relates the amount of charge q which accumulates on surfaces of a substance experiencing a potential difference

q = CV or C = q/V

-Unit in coulomb per volt or farad

-Capacitors in Parallel Ceffective = Ci = C1 + C2 + …+ Cn

 

-Capacitors in Series

__1___ = 1/Ci = _1_ + _1_ + … + _1_ Ceff C1 C2 Cn

For a pair of plates with area A and separated by distance d

d

C = o A/d

The energy stored in a capacitor is

W = [qV]/2 = CV2/2 = q2/2C

The potential difference between the plates of a parallelplate capacitor is

V = Ed,

where E = /o = electric field = surface charge density = q/A

Charges in Motion

Current I = movement of electric charge from oneposition to another. The direction of I is taken as the direction of which positive charges would move.

(in actuality only electrons move)

Electromotive force – any agency which causescurrent to flow; e.g. batteries, electrical outlets

I = q/t or rate at which electric charge flows across a surfaceI in coulomb/sec or ampere

Current is related to voltage by Ohm’s law V = IR,where R = V/I is the resistance in ohm = volt/ampere

How to read Resistor Color CodesFirst the codeBlack 0Brown 1Red 2Orange 3Yellow 4Green 5Blue 6Violet 7Gray 8White 9The mnemonicBad Boys Rape Our Young Girls But Violet Gives Willingly *

First find the tolerance band, it will typically be gold ( 5%) and sometimes silver (10%).Starting from the other end, identify the first band – write down the number associated with that color; in this case Blue is 6.Now 'read' the next color, here it is red so write down a '2' next to the six. (you should have '62' so far.)Now read the third or 'multiplier' band and write down that number of zeros.In this example it is two so we get '6200' or '6,200'. If the 'multiplier' band is Black (for zero) don't write any zeros down.If the 'multiplier' band is Gold move the decimal point one to the left. If the 'multiplier' band is Silver  move the decimal point two places to the left. If the resistor has one more band past the tolerance band it is a quality band.

Read the number as the '% Failure rate per 1000 hour' This is rated assuming full wattagebeing applied to the resistors. (To get better failure rates, resistors are typically specified tohave twice the needed wattage dissipation thatthe circuit produces) 1% resistors have three bands to read digits to the left of the multiplier. They have a different temperature coefficient in order to provide the 1% tolerance.At 1% most error is in the temperature coefficent - ie 20ppm.

Resistors in series

Reff = Ri = R1 + R2 + …+ Rn

 For parallel circuits: 1/ Reff = 1/ Ri = 1/R1 +1/R2 + …+1/Rn

 Resistivity is defined as         = R A/ where A = cross-section area and          = length Conductivity = 1/ = /RA

Kirchoff’s laws:

1. Sum of all currents at any junction is zero

2. The sum of all electromotive forces is equalto the potential drop across each resistor.

Magnetostatics

- magnetic force is a manifestation of the electric force when the charges have relative motion

-Magnetic fields are produced by electric currents,which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz forcelaw. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole.

Information provided by: http://hyperphysics.phy-astr.gsu.edu 

Lorentz force law

-The total force acting on a particle is the sum of the electric and magnetic forces, that is,

F (total) = F (electric) + F (magnetic)

= qE + qv x B

Magnetic ForceThe magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge: The implications of this expression include:1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B.2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magneticfield. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero.3. The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product. From the force relationship above it can be deduced that the units of magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the Earth's magnetic field. A Tesla is 10,000 Gauss. The Earth's magnetic field is on the order of half a Gauss.

Magnetism and its relation to electrical phenomena

Oersted – current carrying wire affects the magnetjust as a magnet affects another magnetic material

e.g. compass needles placed randomly perpendicularto a current-carrying wire will reorient along the magnetic field created by the current

Ampere – current-carrying wire had all the properties of a magnet. He also studied the mutual interactionbetween two current-carrying wires.

Arago – a current-carrying wire could also magnetize apiece of iron

a)

b)

Ampere’s Law

Ampere's lawAmpere's law is the magnetic equivalent of Gauss's law.

Small elements of length Li

a magnetic field Bi at each element.

the sum over elements Li of the magnetic field along the

direction of the element, times the element length, is proportional to the current I that passes through the loop

for a wire, the loop can be a circle drawn around the wire, and since the field is always tangent to the circle, cos = 1. The circumference of the circle of radius r is 2r, therefore Ampere's law becomes

Faraday's Law

Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic fieldstrength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating thecoil relative to the magnet, etc.

Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a succinct summary of the ways a voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

Lenz's LawWhen an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below,if the B field is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant.

Magnetic materials1. Diamagnetism B = H - Bi, Cu, Pb, Hg, Sb H = magnetic intensity• the direction of induced magnetic dipole is opposite the magnetic field2. Paramagnetism B = H - Al, Nd, Pt, Pd • possess permanent magnetic dipole moment 3. Ferromagnetism B H - Fe, Ni, Co, GdWhen a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magneticfield is applied to the material, its magnetization will trace outa loop called a hysteresis loop.

Hysteresis Loop

                                                                                                                                                    

                   

Maxwell’ synthesis of electromagnetic fields

1. Gauss law for electricity related to Coulomb’s law- this relates the E field and its source (enclosed charge)2. Gauss law for magnetism: there is no “magnetic” charge analogous to electric charge3. Faraday’s law of magnetic induction: the induced emf in a loop is equal to the time rate of change of magnetic flux through the loop4. Generalized Ampere’s law: giving the relation of magnetic field and its sources namely current and changing electric field.

Light as an electromagnetic wave

- shows interference- exhibits diffraction-propagates through medium-shows dispersion

-Light, microwaves, x-rays, and TV and radio transmissions are all kinds of electromagnetic waves. They are all the same kind of wavy disturbance that repeats itself over a distance called the wavelength.

Electromagnetic waves are formed when an electric field (shown as blue arrows) couples with a magnetic field (shown as red arrows). The magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave

Waves in the electromagnetic spectrum vary in size from very long radio waves the size of buildings, to very short gamma-rays smaller than the size of the nucleus of an atom.