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:

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, Q1 and Q2, 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 ke is Coulomb's constant (ke = 8.99 × 109 N m2 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
 * FEB = 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
 * FE = Q E

Electric Force will exert a pressure FE / 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
 * $$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}$$