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Electricity
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Unlike sound waves, electrical and electromagnetic waves don’t
need a medium to propagate through. Before the MichelsonMorley interferometer experiment of 1887, scientists believed
that light and other electromagnetic waves travelled through a
medium called “ether.” As a result of this failed experiment (it
failed to show a medium called ether), scientists recognized that
electromagnetic waves can travel through a vacuum.
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Charge is Q = I¢t
The smallest electrical charge is the elementary charge e, the
charge of a single electron. The value of the charge was
determined to good accuracy by Millikan in 1910. In order to
determine the electrical charge, Millikan measured the velocity of
charged oil drops in an electrical field. Improved experiments
determined with even greater accuracy the value of a charge. The
charge has a value of 1.602 £ 10-19 Coulombs. Quarks have even
smaller elementary charge of e/3.
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Electomagnetic waves are agitations of the electromagnetic
field. The electical force is always parallel or antiparallel to
the electric field. The movement of electrical charges is
found in electrical conductors due to the movement of free
electrons and in fluids due to the movement of ions. We
recognize a difference between conductors, insulators, and
semi-conductors. Electrons don’t pile up at the end of a long
telephone line because when you phone someone, you are
sending along an invisible force field which causes the
electrons that are already waiting in your listener’s phone to
move. The electrons themself barely travel, instead the force
field propagates along the telephone line.
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The electrical field
The electrical field can arise due to electrical charges or due to
a changing magnet field. The electrical field is a vector field,
every point in space is given a vector according to the
definition of the electrical field strengths or forces. Electric
fields can be represented by field line pictures. Charges are
influenced by the electrical field. The following force acts on a
charge q
F = qE
For which E is the electric field vector and q is the charge.
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Electric field of a positive charge
Electric field of two equal but opposite charges (electrical dipole)
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Electric Field of Two Like Charges
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Bipolar Field
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Coulomb’s Law
The electric force between two particles with charges of q1 and
q2 separated by a distance r is given by the equation
This is Coulomb’s Law. It is written in terms of a fundamental
constant whose value is approximately
It is an inverse-square law just like for the gravitational force
between two masses. A negative F is interpreted as an
attraction between unlike charges and a positive as a repulsion
between two like charges. Coulomb's law is actually a special
case of Gauss's Law.
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Problem
Consider two small spheres, one carrying a charge of 1 nC
(nanocoulomb or 10-9 Coulomb) and the other a charge of -3
nC, separated by a distance of 4 cm. Find the electric force
between them.
Solution
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Gauss’ Law
Gauss' Law describes the electrical flux through a closed area.
The law uses the concept of flux which is defined for all vector
fields. Imagine a body with a charge of Q which is surrounded
by an orientated, closed area. Orientated just means that there is
an external and internal side. The area can be any form, a sphere
or some kind of balloon. The field lines originating from the
charge flow through this area. Just like water flows through an
area, there is a source and a drain. Because the universe is
electrically neutral, all of the field lines that come from a charge
must end at another opposite charge. The flux of a charge outside
of the area A flows from one side to the other. The total flux thus
depends only on the enclosed charge. The main point of the law
is that the flux equals charge divided by a nature constant.
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Problem
Calculate Gauss’ Law for a point charge q placed at the
center of a sphere.
Solution
dA points radially out for a sphere and for reasons of
symmetry, E must also be directed radially out and constant
in magnet over the surface of a sphere. Thus because E is
parallel to dA and cos µ = 1
and because E is constant over the surface A
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Because the surface area of a sphere is equal to
Hence, Gauss’ Law yields
or
Thus we obtain Coulomb’s Law again.
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Lightning
Lightning arises as a result of the friction in the clouds.
When many small water drops collide in a cloud and
create friction, then an electrical current is produced in
the cloud. You experience the same sort of friction
when your feet rub against the carpeting and cause a
charge when you touch the metal door knob (static
electricity). At some point the voltage between the
clouds is so high that the air becomes a conductor and
the charges flow to the earth. A bolt of lightning occurs
when the electrons jump from a negatively charged area
to a positively charged area.
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Battery
Flow of Anions
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The Battery
A battery consists of portable chemical energie that is
transformed to electrical energy as soon as it is put in
circuit and discharges itself. Most batteries work with a
metal which serves as the minus pole and a metall oxide
that serves as the positive pole. The minus pole is also
called anode and the plus pole is called cathode. An
electrically conducting fluid called the electrolyte bridges
the two poles. In order to avoid a short circuit, the anode
and cathode are divided by a separator made of plastic or
paper. As soon as the battery is placed in a circuit and the
poles are brought into contact the process of electrolysis
takes place.
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