Download Electric Fields

1/25/17
Electric Fields (1)
A. B. Kaye, Ph.D.
Associate Professor of Physics
24 January 2017
Electricity and Magnetism
Why study electricity and magnetism?
• The laws of electricity and magnetism play a
central role in the operation of many modern
devices
• The interatomic and intermolecular forces
responsible for the formation of solids and
liquids are electric in nature
•
This is why you don’t fall through your chair when you sit
on it – even though most of the chair is empty space
Historically speaking…
Chinese
§ Documents suggest that magnetism was observed as early as 2000 BC
Greeks
§ Electrical and magnetic phenomena observed as early as 700 BC
§ In 580 BC, Thales showed that when you rub amber with a piece of cloth,
it became endowed with the power of attracting light bodies to itself
(remained unexplained)
§ Other experiments with magnetite
1600
§ William Gilbert (physician to Queen Elizabeth) showed electrification
effects were not confined to just amber.
§ The electrification effects were a general phenomena.
1
1/25/17
Historically speaking…
1733
§ Charles Francois du Fay discovers that electricity comes in two
kinds, which he called resinous (–) and vitreous (+)
1785
§ Charles Augustin Coulomb confirmed inverse square law form for
electric forces. He also proposes a combined fluid/action-at-adistance theory with two conducting fluids; fighting breaks out
between single– and double-fluid partisans.
1792
§ Alessandro Volta shows that when moisture comes between two
different metals, electricity is created.
• The first example of flowing electricity
Historically speaking…
21 April 1820
§ Hans Christian Ørsted found a compass needle deflected when near a wire carrying
an electric current
• Electricity and magnetism must have a direct relationship
• Andre Marie Ampere shows that parallel currents attract or repel each other depending on the
direction of current flow (opposite currents attract)
1826
§ Georg Simon Ohm establishes the result now known as Ohm’s law:
V=IR
1831
§ Faraday invented a bell that could be rung at a distance using an electric wire in
1831 – a precursor to the modern doorbell
§ Michael Faraday and Joseph Henry (independently) showed that when a magnet is
moved inside a coil of copper wire, a small electric current is generated
• Faraday published his findings first
Historically speaking…
~1870
§ Thomas Alva Edison builds the first practical DC generator.
§ George Westinghouse purchased and develops Nikola Tesla’s patented
motor for generating AC
1873
§ James Clerk Maxwell used observations and other experimental facts as a
basis for formulating the laws of electromagnetism in his Treatise on
Electricity and Magnetism
• Unified electricity and magnetism
See class website for “A Brief History of
Electromagnetism” and “Another Brief History of
Electromagnetism”
2
1/25/17
ELECTRIC FIELDS
Properties of Electric Charges
Electric Charges
• There are two kinds of electric charges
Called “positive” and “negative”
•
•
Negative charges are the type possessed by electrons
•
Positive charges are the type possessed by protons (or positrons)
• Charges of the same sign repel one another and
charges with opposite signs attract one another
• Electric charge is always conserved in an isolated
system
•
E.g., charge is not created in the process of rubbing two objects
together; the electrification is due to the transfer of charge from
one object to the other
Conservation of Electric Charges
• A glass rod is rubbed with silk
• Electrons are transferred from the
glass to the silk; and each electron
adds a negative charge to the silk
• An equal positive charge is left on the
rod
What does this mean?
• “Charge” is not a substance, but is rather
a property that is inferred from observed
interactions
• Right now, we don’t understand what
“charge” is, but we can explain how it
behaves
3
1/25/17
Formal Statement of Charge Conservation
• We can express the conservation of charge using the charge density r (in Coulombs
per cubic meter) and the electric current density J (in Amperes per square meter) as:
•
•
•
The 1st term on the LHS the time rate of change of the charge density at some point in space
The 2nd term on the LHS is the divergence of the current density at the same point
Because these two terms are equal, the only way for r to change if for a current to flow into or out
of the point.
• Can we prove this? Sure we can. The net current flowing into a volume can be
written as:
•
•
•
Here, S = ∂V is the boundary of the volume V oriented by outward-pointing normal vectors
Further, dS is a “shorthand” way of writing NdS – those outward-pointing normal vectors
J is the current density (charge per unit area per unit time) at the surface of the volume; it points in
the direction of the current flow
Derivation (2)
• From the divergence theorem, we can express the current as:
• Conservation of charge means that the net current into the volume must equal the net
change of current within the volume:
(a)
• The total charge q in the volume V is the integral (sum) of the charge density in that
volume:
•
… which means that
(b)
Derivation (3)
• Let’s now set equations (a) and (b) equal to each other (since they are both
expressions for dq/dt):
• Since this must be true for every volume V, we can write
4
1/25/17
Example Problem – Conservation of Charge
•
Two identical metal spheres, separated by some distance and labeled
“A” and “B” are charged; sphere A carries a net charge of +7Q and
sphere B carries of net charge of –3Q.
•
The spheres are brought together, allowed to touch, and then
separated again. What is the charge on each of the spheres after the
separation?
Quantization of Electric Charges
• In 1909, Robert Millikan discovered that charge
always occurs as integral multiples of a
fundamental quantity
Therefore, the electric charge, q, is said to be quantized
q is the standard symbol used for charge as a variable
q = ±Ne
•
•
•
•
N is an integer
•
e is the fundamental unit of charge
•
|e| = 1.6021766208 x 10–19 C
•
Electron: q = –e
•
Proton/Positron: q = +e
ELECTRIC FIELDS
Interesting Problems
5
1/25/17
Interesting Problem #1
• Compare the magnitudes of the gravitational
force of attraction and of the electric force of
attraction between the electron and the proton in
a hydrogen atom.
• According to Newtonian mechanics, what is the
acceleration of the electron?
•
Assume that the distance between these particles in a
hydrogen atom is 5.3 x 10–11 m.
Interesting Problem #2
• A simple electroscope for the
detection and measurement of
electric charge consists of two small
foil-covered cork balls of 1.5 x 10–4
kg each suspended by threads that
are 10 cm long.
• When equal electric charges are
placed on the balls, the electric
repulsive force pushes them apart,
and the angle between the threads
indicates the magnitude of the
electric charge. If the equilibrium
angle between the threads is 60º,
what is the magnitude of the charge?
Interesting Problem #3
• Two point charges +Q and –Q are separated by a distance
d.
• A positive point charge q is equidistant from these charges,
at a distance x from their midpoint.
• What is the electric force F on the point charge q?
6
1/25/17
ELECTRIC FIELDS
Charging Objects by Induction
Types of Materials
If we classify materials by how easy it is to move
electrons through them, then we end up with
three different types:
1. Conductors
2. Insulators
3. Semiconductors
Let’s look at each one of these in more detail
Conductors
• Electrical conductors are materials in which
some of the electrons are free electrons
•
•
•
Free electrons are “not bound” to the atoms; the electrons
can move relatively freely through the material
When a good conductor is charged in a small region, the
charge readily distributes itself over the entire surface of
the material
The best five conducting materials are:
1.
Silver
2.
Copper
3.
Gold
4.
Aluminum
5.
Zinc
7
1/25/17
Insulators
• Electrical insulators are materials in which all
of the electrons are bound to atoms
These electrons can not move relatively freely through the
material
When a good insulator is charged in a small region, the
charge is unable to move to other regions of the material
Examples of good insulators:
•
•
•
•
Teflon
•
PVC and other plastics
•
Ceramics/porcelain
•
Paper/cardboard
•
Rubber
•
Air
Semiconductors
• The electrical properties of semiconductors are
somewhere between those of insulators and
conductors
• Examples of semiconductor materials include
silicon and germanium
•
Semiconductors made from these materials are commonly used in
making electronic chips
• The electrical properties of semiconductors can be
changed by the addition of controlled amounts of
certain atoms to the material in a process called
“doping”
There are three ways to give an object a net charge
1. Charging by friction – This is useful for charging insulators. If you
rub one material with another (say, a plastic ruler with a piece of
paper towel), electrons have a tendency to be transferred from one
material to the other. For example, rubbing glass with silk or saran
wrap generally leaves the glass with a positive charge; rubbing a
PVC rod with fur generally gives the rod a negative charge.
2. Charging by conduction – Useful for charging metals and other
conductors. If a charged object touches a conductor, some charge will
be transferred between the object and the conductor, charging the
conductor with the same sign as the charge on the object.
3. Charging by induction (example follows)
8
1/25/17
Charging by Induction
•
Charging by induction
requires no contact with the
object inducing the charge
•
Assume we start with a
neutral metallic sphere.
•
•
The sphere has the same number
of positive and negative charges
A charged rubber rod is placed
near the sphere
•
•
It does not touch the sphere
The electrons in the neutral
sphere are redistributed
Charging by Induction (con’t)
•
The sphere is grounded
•
•
Some electrons can leave the
sphere through the ground wire
The ground wire is removed
•
•
There will now be more positive
charges that are not uniformly
distributed
The positive charge has been
induced in the sphere
Charging by Induction (con’t)
• The rod is removed
•
•
The electrons remaining on
the sphere redistribute
themselves and there is still
a net positive charge on the
sphere
The charge is now uniformly
distributed
9
1/25/17
Charge Rearrangement in Insulators
• A process similar to
induction can take place in
insulators
•
The charges within the
molecules of the material are
rearranged
Why does static electricity seem more apparent in winter?
• In the winter, we see static electricity in many places:
•
•
•
•
Taking clothes out of the dryer
Taking a sweater off
Combing/brushing your hair
Getting a shock from a doorknob (or something else) after
walking on carpet
• Why is this more obvious in winter?
•
•
•
The air is much drier, and dry air is a good insulator
That means once you charge something it will tend to stay
charged (until it finds a way to discharge!)
In more humid conditions, the water molecules in the air (which
are polarized) will tend to remove excess charge quickly
10