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Lecture 1
Introduction
Electricity and Magnetism are all around us. Not only in the devices we use every day
(cell phones, computers etc.) but almost everything we see happening around us is due
to electricity and magnetism. For example:
Atoms and molecules are held together by electric forces
and therefore chemical reactions occur because of electric forces
Light is an electromagnetic wave, so we learn about the world also using electric forces.
Atoms in solids are also held together by electric forces.
In fact the only other force we experience is gravity. Everything else is electricity and
magnetism.
• In physics we learn by measuring. The most
basic measurement: SIZE
• Why? Because objects behave differently at
different scales, the forces that act are
different.
Quantum Mechanics
Electricity and Magnetism
Nuclear
Radioactivity
Newtonian/Einstein
Dark Matter (83%!!)
and Dark Energy
Gravity
Aside: Prefixes and notations for large
and small quantities
Factor
prefix
Abbr.
10-15
femto
f
10-12
pico
p
10-9
nano
n
10-6
micro
m
10-3
milli
m
103
kilo
K
106
mega
M
109
giga
G
1012
tera
T
1
Gravity
• Law of Gravity: (Newton)
Two bodies attract each other with a force proportional
to the product of their masses and inversely proportional
to the square of their distances.
Greatest achievement?
Discovering the law of gravity is possibly one of the
greatest achievements of humankind.
What do you think?
A.
B.
C.
D.
Going to the Moon
Invention of computers
Mapping of DNA
Other
Problem
Using that (these are approximate numbers)
• the radius of the Earth is 6000Km
• the acceleration of gravity on
the surface is 10 m/s2
• the density of the Earth is five times that of
water
• Estimate the value of Newton’s constant G
Problem
Using that the period of the Moon is
approximately one month, estimate the
distance from the Earth to the Moon.
How can you use that to know the size of the
Moon?
HOw can you use that to estimate the time it
takes a rocket to reach the Moon?
Lecture 2
Review question
What’s the size of an atom?
A.
B.
C.
D.
10-15 m
10-10 m
10-3 m
1m
Lecture 2
Electrostatics: Charge and fields
Electrostatics describes the interactions of electric charges in the same way that gravity
describes the interactions of masses. It follows Coulomb’s law:
Crucial difference: The force can be attractive or repulsive.
1. Charges of the same sign repel each other. Of opposite sign attract each other.
2. Charges add up with sign. So, two charges of opposite sign and equal magnitude
cancel each other producing a neutral object which feels no electric force.
3. Charge is conserved, it cannot be created or destroyed.
4.
C means Coulomb, unit of electric charge.
Some considerations:
• Why statics? If charges move, they create also magnetic fields,
that are important if the charges move close to the speed of
light, or we have many charges moving together (electric
current). Is there a similar effect in gravity?
• Minimal electric charge:
Electron:
• The charge of the proton has the same value but opposite
sign. Why?
• Atoms are exactly neutral, however there are residual forces.
• These residual forces are responsible for most phenomena we
see in Nature. There are exceptions, for example lightning.
• On the other hand we have learned to use special materials
like metals, insulators, semiconductors, superconductors, etc.
to use electric (and magnetic) forces to our advantage.
Conductors and insulators
• Conductors allow charges to move freely inside them.
• Insulators can be charged by friction for example, but
charges stay fixed in the same place.
• Since charges of the same sign repel each other, in a
conductor charges migrate to the surface.
• We can charge a conductor using an interesting
phenomenon called induction.
Q=0
Charged insulator
Total charge is CONSERVED. Therefore the conductor
acquires no charge. What to do? We need to bring
charge from somewhere else!.
Connections to ground: an infinite reservoir of charge. Connecting circuits to ground makes
them more stable and safe. It should always be done when possible.
Electric field
Electricity is not just forces between charges. Light and radio waves are
examples of how electric phenomena can propagate and exist
independently of charges.
The electric field is a vector and can be detected by putting a test charge
which will feel a force:
Principle of superposition: Electric fields from different sources add up as
vectors.
This implies the principle of superposition for forces:
Clicker question
Given the formula
, in which units is
the Electric Field measured?
1.
2.
3.
4.
N (Newtons)
N/C (Newtons / Coulomb)
N C (Newtons . Coulombs)
V/m (Volts / meters)
• Addition of vectors
Simple example: displacements. We move 30m to the
North, then 20 meters East and then 10m SW:
1
1
(0,30)  (20,0) 10(
,
)
2
2
10
10
 (20 
,30 
)
2
2
 (12.93,22.93)
tan  
22.93
12.93
L  12.932  22.932
Lecture 3
Review question
Besides the Coulomb law,
other effects appear if:
A.
B.
C.
D.
Charges are very large.
Charges are moving fast.
Charges are very far away from each other.
Charges are very close to each other.
Lecture 3
Electrostatics: Electric field / Energy
The Electric field is a vector field. It defines a vector at each point in
space. Drawing an arrow at (a few) points in space is one option to
represent vector fields graphically. Another is to draw lines which, at
each point are parallel to the electric field. They area called “lines of
electric field”
Vector fields are everywhere. Example, motion of air, the velocity is a
vector field. The lines are now lines of flow which indicate how air
moves.
Electric field of a spherical charge
Electric field is measured in N/C
Dipole: Two charges of equal absolute value but opposite sign.
Lines of electric field start from positive charges and
end in negative charges
Generating electricity: Kelvin generator
Clicker question
Where is the energy to light the bulbs coming from?
A.
B.
C.
D.
Hidden battery
Friction
Water
Gravity
Hint: When will it stop working? and what do you
have to do to make it work again?
Energy is always conserved!
You can convert one type of energy into another:
Wind
Gravity
electricity (wind mill)
electricity (hydroelectric dam)
Don’t confuse Energy with Power.
Power is Energy produced (or consumed) per unit time.
Units of Energy: J (Joules) = N m = Kg m2/s2
Units of Power: W (Watts) = J/s
In Newtonian mechanics, forces can be derived from
potentials
electrostatic potential
Work:
[ If there is an angle between force and displacement, we multiply by
the cosine of the angle ]
To reproduce Coulomb’s law we need
• Proposal:
• Verification:
We need to use:
as we wanted!.
to get
Lecture 4
Electrostatic potential
In the same way we defined Electric field from the force we
define electrostatic potential from the potential energy.
units: V (Volt)
For a charged particle (or a charged sphere):
The potential decreases along the lines of electric field.
V1
E
V2
V1>V2
Clicker question
Electrostatic potential is measured in Volts which, in
view of the formula
, is the same
as:
A.
B.
C.
D.
N/C
N m /C
NC/m
Nm2 /C
Hint: Remember U is energy, same units as work
W = F Dx
Some comments
• Principle of superposition:
V = V1 + … + Vn as scalars (numbers)
• Constant electric field
• Equipotential surfaces: Surfaces of constant
potential. Perpendicular to the electric field. E.g.
the surface of a conductor (static case).
Potential of a spherical
conductor
For a point charge we said:
Equipotential surfaces are concentric spheres. (V is constant if r is
constant)
If it is a charged sphere, then the potential outside is the same
If it is a conductor there is no electric field inside (in the static case)
and therefore inside the potential is constant (no work needed to
move a probe charge).
In pictures:
E(r)
Notice V is continuous but
E can jump
An interesting problem:
Two conducting spheres of different radii are charged and in
contact. Which one has the largest charge?.
Solution:
The spheres are in contact so they form a single
conductor, the potential has to be the same:
Therefore (V1=V2)
Notice the electric field
So:
If one sphere is very small the electric field is huge!!
Lightning rod.
We said many times that the potential inside a conductor is
constant, no electric field. This is true even is there is hole in it
(with no charge).
Therefore conductors can act as shields.
This is known as Faraday cage and it is extremely important in
applications. For example to insulate delicate electronic
devices. Or for “secrecy”, stopping cell phones, etc.
Electric flux
An important idea in physics (and science) is to use analogous
concepts to describe different phenomena. Example: vector field.
When a vector field represent motion of air an important concept is
that of flow, how much air goes through a surface. It is given by:
If we replace velocity by electric field we obtain the
Electric Flux through a surface. It is easiest to compute if
the surface is everywhere perpendicular to the field.
Equipotentials!
Case of sphere
Gauss law: Total electric flux through a
closed surface is equal to the total charge
enclosed by the surface divided by e0
Further check, consider a truncated cone, the flux
is the same but opposite on the two “lids”.
Therefore the total flux is zero. OK, no charge
inside!
Application: Field of a charged plane with charge
density s (Q= sA). Useful later for capacitors.