Download Electricity, Electric Fields, Current, Voltage, Resistance

Electricity
Electricity is a force much like gravity but millions of time more powerful. Unlike gravity, electricity can be attractive and repulsive.
There are two types of electric charge which are labeled positive
and negative. Like charges (two positive or two negative charges)
repel one another. Unlike charges (one positive and one negative)
attract one another.
All common matter is made up of atoms. At the center of an atom
is the positive nucleus consisting of protons with a positive charge
and neutrons without a charge. ’Orbiting’ around the nucleus are
electrons which have a negative charge. The amount of charge on the
proton is exactly equal to the charge on the electron. The electric
attraction between the positive nucleus and negative electrons hold
the atom together. For example, Helium has two positive protons in
the nucleus and two negative electrons in orbit around the nucleus.
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Electrons have a very small mass (9.1 x 10−31 kg). A proton is
much more massive (1.67 x 10−27) or about 1800 times the mass of
the electron. Because the nucleus is so much more massive than the
the electron, it is normally the electrons that move around.
If an atom loses or gains one or more electrons, it is called an ion.
If you walk across a carpet on a day with low humidity, you can rub
some of the electrons off of your shoes.
You build up a charge and when you touch something, electrons
are attracted to your lack of electrons in the form of a spark. This
also happens when you dry your clothes. As the clothes (especially
synthetic fabrics) tumble after they are dry, they acquire a charge.
You can then get a static discharge when you touch them.
Charge is measured in a unit called a ’Coulomb (C)’. The electron
(or proton) has a charge of magnitude 1.6 x 10−19C. Said another
way, a Coulomb is the charge of 6.25 x 1018 electrons.
The origins of the Coulomb unit go back to chemistry and the early
study of electricity before the atomic nature of matter was understood. The Coulomb is a SI (metric) unit but there is no ’English”
unit of charge. For things electrical, the entire world uses metric
units.
Coulomb’s Law
Coulomb’s Law tells us the force between two charges. It very much
resembles Newton’s law of gravity but the masses are replaced by
charges and the proportionality constant is different. Coulomb’s law
is:
F=k
q1 q2
r2
The force, F, is in Newtons and the charges q1 and q2 are in Coulombs.
The distance, r, is in meters. The proportionality constant is:
k = 8.988 x 109 N m2/C2
k is sometimes called ’Coulomb’s constant’. It is very big compared
to G. Two like charges, each of charge 1 C, placed 1 meter apart will
repel each other with a force of about 9 x 109 Newtons.
Charge Polarization
If a charged object, say with a positive charge, is placed near an
uncharged object, the positive charge attracts some of the electrons in the uncharged object to the side of the object nearer to the
charged object. This is called charge induction.
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While the uncharged object has not total charge (we have not
added or removed charge from the uncharged object) we have rearranged the charge on the object. Such an object is said to be
electrically polarized. There are many things in nature e.g. a water
molecule, that exhibit this type of charge arrangement.
If the humidity is low and your laundry becomes charged with
static electricity, you may have seen a statically charged piece of
clothing like a sock ’jump’ to an uncharged object like a wall or you.
If the sock has a negative charge, it ’pulls’ a positive charge to the
side of the uncharged object. In fact, the ’pull’ is actually a ’pushing’
of some of the electrons away from the part of the object near the
negatively charged sock.
Making a Static charge
Building up a static charge is more complicated than simply ’rubbing’ electrons off of one object to another. This does occur but
the effect is normally very small. The materials that are in contact
determine how much charge can be accumulated.
The chemical potential of the material determines how strong the
material’s atoms hold on to their electrons. (Some elements like
chlorine hold on very tightly to their electrons and will even ’steal’
them from other atoms. Other elements like many metals only loosely
hold on to some of their electrons and will give up or trade them
freely). Depending on the material being in contact, free electrons
can be transferred from one material to the other. The rubbing gives
many opportunities for this transfer to take place. The process is
self-limiting. Once one surface becomes charged with an excess of
electrons, the accumulated negative charge repeals other electrons
trying to add to the negative charge.
’Photo’ copies
Photocopiers use static electricity to make copies. The key to the
process is a belt or cylinder of a material which is a photo-conductor.
A photo-conductor is normally an insulator but becomes conducting
when exposed to light. The process starts when the photo-conductor
is charged by a negative corona discharge (a uniform spray of charge
from many fine wires). An optical image of the document to be copied
is projected on the charged photo-conductor. Where the light (white
part of the image) hits the photo-conductor, the photo-conductor
becomes a conductor and the charge is neutralized.
The remaining part of the process is transferring the (black) image
to the plain paper. Since the black part of the image on the photoconductor is still charged, fine positive toner particles are attracted
to the negatively charged areas. At this point, a lamp discharges the
photo-conductor and the image is transferred to plain paper. The fine
toner particles are then bonded to the paper by heat (or chemicals).
Electric Fields
Like gravity, a charge fields the influence of another charge at a
distance. We can use the idea of an electric field to visualize
the force field around a charge, group of charges or even a charge
distribution. The field lines at a given point in space tell us the
direction a very small positive charge would move if placed at that
point. Thus the lines always point away from a positive charge and
towards a negative charge.
The electric field is defined by:
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E
F~
q
The units of the electric field is Newton per Coulomb (N/C). From
Coulomb’s Law and the definition of the electric field, the magnitude
of the electric field for a point charge is given by
E = k rq2
The ’Corona’ discharge for the photocopier utilizes this feature of
a point charge electric field. As you approach a small point at the
end of a wire or surface, the electric field lines concentrate creating
a region of strong electric fields near the point. This allows for a
discharge because the electric field is strong enough to ionize the air
and create a discharge.
Other charge distributions have more complicated electric fields
which depend on the geometry of the charge distribution.
For a single positive charge, the electric field lines point radially away
from the point charge. For a positive and negative charge, the pattern
is called a dipole. For two sheets of charge, the pattern is a series
of uniformly spaced lines.
Gravity and electricity are examples of a field. A field is just a
way of thinking about the force. The force pervades all of space. The
earth does not touch the moon but we know it pulls (exerts a force)
on the moon. This is called force or action at a distance. Even
if there is not a charged object at a point in space, we know there
would be a force on a charge object from the electrostatic attraction.
The direction and magnitude of this imaginary pull at any point is
how we think of the field.
Actually, this idea of ’action at a distance’ has some problems.
How do we really know the charged object (or massive object for
gravity) is really there? What if it moved very quickly to another
location.
Although they are called ’quantum field’ theories, in modern (quantum) physics every force is transmitted by sending a force particle
(boson) between the two particles feeling the force. In this way,
modern physics avoids the problems of ’action at a distance’.
Electric Potential
Just as we spoke of a mass having gravitational potential energy in
a gravitational field, an electric charge in an electric field also has
potential energy. Because the energy depends on position (and not
motion) this is potential energy. A larger charge at the same position
as a smaller charge in an electric field will have more potential energy.
To avoid dealing with total energy depending on the charge, we define
the electric potential as:
electric potential =
electric potential energy
amount of charge
The unit of electric potential is the Volt (V). It is defined as:
1 volt =
1 Joule
Coulomb
Electric potential gives us a way to determine the electrical effects
at a location in space even if there is not a charge present at that
location. Often we speak of potential difference. This is just the
difference in electrical potential between two given points.
Electric potential can be related to the electric field by:
electric field magnitude =
∆V
∆r
The direction of the electric field is given by the direction which has
the largest change in the voltage change (gradient).
There are many ways to produce a potential difference between
two points. A battery produces a potential difference between the
two terminals of the battery by chemical means. A power station
produces a (varying) potential difference between the wires on the
power grid. A power station produces the electrical potential by
induction which we will discuss when we talk about magnets and
magnetic fields.
Electric Current
When a potential difference is applied across a conducting wire, the
electrons move towards the positive terminal and way from the negative terminal. In conductors (normally a metal) there are electrons
which can move freely inside the conductor. (A ’bad’ conductor is
called an insulator analogous to heat flow). A flowing of electric
charge is called a current. The wire does not become charged since
the electrons are simply moving around the closed circuit under the influence of the potential difference supplied by the voltage
source.
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By convention we say the current is flowing from the positive terminal
to the negative terminal of the battery. This is backwards to
the electron flow. This convention was defined before people
knew about free electrons in metals or even understood atoms.
You can think of the flow of charge much like the flowing of water
in a pipe. In this analogy the battery is a pump, the pump pressure
is the potential difference, the wires are the pipes and the flow rate
is the current.
This current (flow rate of charge) is measured in amperes. An
ampere is a Coulomb of charge flowing past a point in the circuit
(through the cross-section of the wire) in one second.
Resistance
Some conductors provide an good path of the charge to flow (a big
pipe in our water analogy), others obstruct the flow to some extent
(a narrow pipe). Electrical resistance is how well a current can
flow through something. A wire which will allow only a small current
to pass through it is said to have a high resistance. Resistance is
measured in Ohms (Ω). If a large potential difference is applied to
given conductor, more current will flow. In our water analogy this is
like increasing the water pressure. More water will flow through the
same pipe if you up the pressure. This is embodied in Ohm’s Law:
current =
voltage
resistance
or V = IR
where V is the voltage (potential difference), I is the current and R
is the resistance (Ω).
In terms of units:
amperes =
volts
Ω
Ohm’s law lets us find current, voltage or resistance when we know
two two of these values.
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We can analyze a common flashlight using Ohm’s law. The filament is a thin tungsten wire as we discussed earlier. The filament
is very thin and tungsten is not an excellent conductor like copper
or aluminum. The resistance of the filament in the bulb is ≈ 20Ω.
When the switch is closed current can flow in a closed circuit around
the batteries and through the bulb. Each battery is 1.5 volts. The
two batteries in series give 3 volts. From Ohm’s law, the current is 3
volts/20Ω or 0.15 amperes.
Electrical Power
Power (energy or work per time) is normally expressed in watts.
With an electrical circuit, the power output of the voltage source is
given by:
Power = current x voltage
or said in terms of the units:
Watt = ampere x volt
A 60 Watt electrical bulb operating at 120 volts draws 1/2 ampere
of current from the electrical outlet. For our flashlight, the power is
3 volts times 0.15 amperes or 0.45 watts.
This should not be too much of a surprise since current is Coulombs/second
and volts are Joules/Coulomb. Multiplied together you get Joules/second
which is, of course, a watt.