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ELECTROSTATICS
2 TYPES: positive (e.g. glass rod rubbed with
silk) and negative (e.g. rubber rod rubbed with
fur)
Law governing charges:
a. two charges of same electrification repel;
while unlike charges attract
b. charge is conserved in an isolated system
Unit of Charge: in multiples of
e = 1.6 x 10-19 coulomb
Conductors, Insulators, Semiconductors
Conductors – capacity to allow motion of charges
Insulators- passive substances as far as charge
motion is concerned
Semiconductors – 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 the
distance between them F = k qq’/r2
k = 9 x 109 nt – m2/coul2
q
q’
r
k = 1/4 o
o = permittivity of free space
-19
2
2
= 8.8542 x 10
coul /nt-m
Electric field
A field of force or electric field intensity is set up in
the 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
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 from
a source charge Q is U = 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___
Ceff
=  1/Ci = _1_ + _1_ + … + _1_
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 parallel
plate capacitor is
V = Ed,
where
E = /o = electric field
= surface charge density = q/A
Charges in Motion
Current I = movement of electric charge from one
position 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 causes
current to flow; e.g. batteries, electrical outlets
I = q/t or rate at which electric charge flows
across a surface
I 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 Codes
First the code
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
The mnemonic
Bad 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 wattage
being applied to the resistors. (To get better
failure rates, resistors are typically specified to
have twice the needed wattage dissipation that
the 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
= R A/
where A = cross-section area and

= length
Conductivity  = 1/r = /RA
Kirchoff’s laws:
1. Sum of all currents at any junction is zero
2. The sum of all electromotive forces is equal
to 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 force
law. 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 Force
The 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 magnetic
field. 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
Magnetism and its relation to electrical phenomena
Oersted – current carrying wire affects the magnet
just as a magnet affects another magnetic material
e.g. compass needles placed randomly perpendicular
to 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 interaction
between two current-carrying wires.
Arago – a current-carrying wire could also magnetize a
piece of iron
Ampere’s Law
a)
b)
Ampere's law
Ampere'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 proportion
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, cosq = 1.
The circumference of the circle of radius r is 2r, 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 field
strength, moving a magnet toward or away from the coil,
moving the coil into or out of the magnetic field, rotating the
coil 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 Law
When 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 materials
1. Diamagnetism
B = H
H = magnetic intensity
- Bi, Cu, Pb, Hg, Sb
• the direction of induced magnetic dipole is
opposite the magnetic field
2. Paramagnetism
B = H
3. Ferromagnetism
- Fe, Ni, Co, Gd
B  H
- Al, Nd, Pt, Pd
• possess permanent magnetic dipole moment
When 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 magnetic
field is applied to the material, its magnetization will trace out
a 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 charge
3. 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 loop
4. 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.