Download Summary of Static Electricity

Summary of Static Electricity
There are four fundamental forces in the universe. They are all field forces meaning that they do
not involve items actually touching.
1. The first and weakest is gravity. Discovered by Newton and the numerical value of the constant
GM1m2
was found experimentally by Cavendish. Fg =
d2
Kq q
2. The second is the electro-magnetic force. First discovered by Coulomb. Fel = 12 2
d
3. The weak nuclear force is responsible for radioactive decay. Most scientists now believe that
the electro-magnetic force and the weak force are actually the same force.
4. The last and strongest force is the strong nuclear force. It holds the nucleus together.
As far as static electricity is concerned, you are concerned with the following quantities:
charge, force, electric field strength, potential difference (voltage), potential energy, and
capacitance.
1. Charge. Charge is measured in Coulombs and is caused by having unequal numbers of
protons and electrons. Q = nexcess ´1.6E -19. Because 1.6 E-19 is the charge of a proton (if it were
negative, then it would be the charge of an electron).
Kq q
2. Electric force. Fel = 12 2 Force is measured in Newtons. All distances must be in meters.
d
This is an inverse square law which means that the force is inversely proportional to the distance
squared. So, if you double the distance, the force is cut to ¼ of its original value. Electric force is a
vector so the signs of E can be determined using normal vector conventions, i.e. east, north, and
up are positive and west, south, and down are negative.
3. Electric field strength is a measure of the effect on a positive test charge. It can be calculated
KQq
2
kq
F
F
KQ
in one of two ways: E = 2 or E = because E = = d = 2 .
q
d
q
q
d
You decide which equation to use based on what information you are given. The unit is Newton
per Coulomb. (N/C) Electric field is a vector so the signs of E can be determined using normal
vector conventions, i.e. east, north, and up are positive and west, south, and down are negative.
The other thing to be aware of is that both vectors ( E, F ) are inverse square laws with d2 in the
denominator. All of the scalars will have only d in the bottom.
4. Potential difference (voltage) is a measure of the work (Joule) per unit charge to move a charge
W
from an infinite distance to its current location. It can be calculated several ways: V =
where
q
kq
W=work in joules. Normally, for a point charge, voltage is calculated as V = . If you are moving
d
a charge through a uniform electric field, then the equation that is most convenient to use is
V = Ed. Technically, the displacement must be in the same direction as the electric field lines. So,
KQq
*d
2
W F *d
KQ
that led you to the
= d
=
V = Edcosq . Also if you think about the fact that V = =
q
q
q
d
first point charge equation. But you could also approach it from an electric field stand point:
V=
F*d
F
F * d (E * q)d
and E = or F = E * q . So, V =
=
= Ed .
q
q
q
q
Furthermore, voltage is a scalar. So, when doing calculations you MUST include the sign of the
charge that you are dealing with.
5. Potential energy is how much energy is stored by placing a charge in a particlular location.
Kq q
PE electric = 1 2 . It can also be calculated by multiplying the voltage by the charge. PE electric = qV .
d
Again, it is a scalar so you must pay attention to the signs of the charges. Although it may be
convenient to think about electrical potential energy as being analogous to gravitational potential
energy. Whenever a charge moves in its ‘natural direction’ it will lose potential energy (negative
PE) and gain KE because the new energy will not change. Conversely, if you move a charge
against its natural tendency you must ADD potential energy. Compare it to gravity. The natural
tendency of a mass is to fall towards the Earth. When it falls, it loses PE g and gains KE.
Conversely, when a mass goes upward (like a ball thrown straight up), it will lose KE and gain PEg
until it stops when PE is at a maximum and TME is equal to PE.
For electric potential energy (PEel), everything is considered based on bringing the test charge in
from an infinitely far away location. So, consider that I have a positive charge sitting at the origin of
a graph. If I try to bring a positive charge in from infinity, the charges should repel. So you are
bringing the charge against its natural tendency so it will gain PEel and slow to a stop. At some
point, it should stop and reverse direction (think like Rutherford’s Gold foil Experiment).
6. Capacitors are pairs of parallel conducting plates that are separated by a small gap.
Capacitance is measured in Farads (F) named after Michael Faraday. Most real life capacitors are
q
measured in microfarads or nanofarads. C = . But capacitance is actually a function of how you
V
eA
make the capacitor rather than the charge and voltage you try to store in the capacitor. C = o . A
d
is the surface area of the plates and d is the distance between the plates. The purpose of a
capacitor is to store energy for later use. So,
PE electric = .5CV 2 The other thing to consider when you are looking at capacitors is whether the
capacitor is still hooked to a Voltage source (a battery). If it is hooked to a voltage source, then the
Voltage is constant but there is a virtually unlimited supply of electrons (charge,q). However, if the
Voltage source is disconnected, there is no source of electrons so q becomes a constant and
voltage will vary.
eo A
q
eA q
, by the transitive property of equality o = which I could rearrange to
d
V
d
V
eo AV = qd . Then I could analyze whether things were directly related (on opposite sides of the
equation) or inversely related (on the same side of the equation)
Since C =
and C =