# Physics Study Guide/Theories of Electricity

## Intro

All atoms are made of charged particles called electrons, neutrons and
protons. At the center of each atom is a nucleus of neutrons and
protons, which is surrounded by electrons orbiting it on circular paths.

## Charged Particles

The three main subatomic particles have very different properties, the
most important of which are:

  Particle   Charge           Mass (kg)
  ---------- ---------------- ----------------
  Electron   negative ( - )   9.11 x 10^-31^
  Proton     positive ( + )   1.67 x 10^-27^
  Neutron    zero ( 0 )       1.67 x 10^-27^

## Charge

Most objects are electrically neutral, i.e. the sum of their electric
charges equal to zero. However, when an object loses or gains electrons
it will become positively or negatively charged, respectively:

:;object + electron → negatively charged object

:;object - electron → positively charged object

A positively charged object has a quantity of charge *+Q* and electric
field lines radiate outward. A negatively charged object has a quantity
of charge *-Q* and electric field lines radiate inward.

**Like charges will repel each other and opposite charges will
attract**, i.e. negatively charged objects attract positively charged
objects and vice versa.

## Electrostatic/Coulomb Force

The force between 2 stationary charges is called the electrostatic force
or Coulomb force.

If two charges, *Q~1~* and *Q~2~*, are at a distance *r* from each
other, they will interact with a force:

:; $F = k_e \frac{Q_1 Q_2}{r^2}$ ,

where *k~e~* is Coulomb\'s constant (*k~e~* = 8.99 × 10^9^ N m^2^
C^−2^). The force of interaction between the charges is attractive if
the charges are opposite signed and repulsive if like signed.

The electrostatic force from a charge will be experienced by any other
charge around it, and the strength and direction of this force at all
positions around the charge is known as the electric field E. The
electric field is directly proportional to the force:

:   $E = \frac {F}{Q}$

## Electromotive Force

When a moving charge passes through a magnetic field, perpendicular to
the field lines,that has direction from left to right. The magnetic
field exerts a force on the charge to make it go up or down. Positive
charge goes up, Negative charge goes down.

:   $\mathbf{F_B} = Q(\mathbf{v} \times \mathbf{B})$

## Electromagnetic Force

For a moving charge the sum of Electrostatic Force and the Electromotive
Force gives Electromagnetic Force acting on the charge

:   F~EB~ = Q E + Q V B = Q (E + V B)

Electrostatic Force is the force generates Current going from left to
right . Electromotive Force is the force generates Current going
perpendicular to current of electrostatic

Electromagnetic Force generates an Electric Field going from left to
right and a magnetic Field perpendicular to Electric Fields

Electromagnetic force may be carried out by Electromagnetic induction
which is the inducing of current using electricity

## Electricity and Conductors

In all conductors, charges move freely in any direction. If there is an
Electric Force

:; F~E~ = Q E

Electric Force will exert a pressure F~E~ / A that force charges in
conductor to move in a straight line. This action generates a current of
charge moving in a straight line.

The Pressure from the Electric Force is called Voltage and the straight
line of moving charges is called Current.

If Voltage is V and Current is I, then the ratio of Current over Voltage
gives the Conductance of the Conductor and the ratio of Voltage over
Current gives the Resistance of the conductor.

:; $G = \frac{I}{V}$\

:; $Z = \frac{V}{I}$

Therefore, *All conductors have a Resistance and a Conductance*

If there exists a straight line conductor of length l, that has surface
area A with conductivity ρ then the Conductance of the conductor

:;G = ρ $\frac{l}{A}$

From above,

$$G = \frac{I}{V}$$ = ρ $\frac{l}{A}$

Therefore, the conduction of all material can be calculated by

:;ρ = $\frac{I}{V} \frac{A}{l}$

## Resistor

If there exists a straight line conductor. As shown above, every
conductor has a Resistance R equal to the ratio of Voltage over Current

$$R = \frac {V}{I}$$

:;$I_R = \frac{V}{R}$

A straight line conductor has a capability of reducing current. This can
be used in an electric circuit to reduce current. In an electric
circuit, straight line conductor has a symbol \--\^\^\^\-- with a
resistance R measured in Ohms Ώ and is called a resistor.

Resistance can be connected in series or in parallel to increase
Resistance or to decrease resistance.

If there are n resistors connected in a series, the total resistance is

:; $R_t = R_1 + R_2 + ... + R_n$

If there are n resistors connected in parallel, then the total
resistance is

:; $\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$

