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Electricity

$F={\frac {k\cdot q_{1}\cdot q_{2}}{r^{2}}}$

The force resulting from two nearby charges is equal to k times charge one times charge two divided by the square of the distance between the charges. This what force of attraction between to charged particle says, according to coulomb's law.

$E={\frac {F}{q}}$

The electric field created by a charge is equal to the force generated divided by the charge.

$E={\frac {k\cdot q}{r^{2}}}$

Electric field is equal to a constant, “k”, times the charge divided by the square of the distance between the charge and the point in question.

$U={\frac {k\cdot q_{1}\cdot q_{2}}{r}}$

Electric potential energy is equal to a constant, “k” multiplied by the two charges and divided by the distance between the charges.

Variables

F: Force (N)
k: a constant, 8.988×10⁹ (N·m²/C²)
q₁: charge one (C)
q₂: charge two (C)
r: distance between the two charges, (m)

Electricity acts as if all matter were divided into four categories:

Superconductors, which allow current to flow with no resistance. (However these have only been produced in relatively extreme laboratory conditions, such as at temperatures approaching absolute zero)
Conductors, which allow electric current to flow with little resistance.
Semiconductors, which allow some electric current to flow but with significant resistance.
Insulators, which do not allow electric current to flow.

Charges are positive (+) or negative (-). Any two like charges repel each other, and opposite charges attract each other.

Electric fields

A charge in an electrical field feels a force. The charge is not a vector, but force is a vector, and so is the electric field. If a charge is positive, then force and the electric field point in the same direction. If the charge is negative, then the electric field and force vectors point in opposite directions.

A point charge in space causes an electric field. The field is stronger closer to the point and weaker farther away.

Electricity is made of subatomic particles called Electrons and so are Electric Fields and Magnetic Fields. One must also note that electrical fields come under the category of spherical fields as the inverse square law may be applied to the electrical field. This means that the electrical force, exhibited by the electrical field emitted by the subatomic electron charge (-), acting upon a body is inversely proportional to the distance between the center point of the electric field (subatomic electron) and the body on which the electric force is acting upon.

An electric circuit is composed of conducting wires (through which an electric current flows through), a key or switch which is utilized to open and close the circuit, components which transfer electrical energy to a form of energy required by the component and an electromotive source (such as a voltaic cell). A voltaic cell is an electromotive source in which are present two plates, zinc and copper, placed in dilute sulphuric acid. Whence the circuit is closed the zinc reacts with the sulphuric acid to produce zinc sulphate. The electromotive force which discharges the electrical energy in the electric current is considered to be originated on the surface of the zinc plate in the voltaic cell. However, depending upon the cell, closing the circuit gives rise to polarization, accumulation of hydrogen bubbles on the surface of the copper plate which seriously interferes with the movement of electricity and reduces the magnitude of the electromotive force. For this reason Leclanché cells are utilized. Consisting of similar characteristics as that of the voltaic cell however a Mage difference is present. Instead of the use of copper plates, a carbon plate is used. For this reason, magneze dioxide may be placed on the carbon to react to form a compound which whence in contact with hydrogen bubbles will turn the hydrogen into water, hence increasing the size of the electromotive force produced by the cell. The resistance encountered in conducting wires: Inversely proportional to the diameter of the conducting wire. Directly proportional to the length of the conducting wire. Varies with different substances. Varies with temperature of the conducting wire.

In order to maintain a constant flow of an electric current a constant expenditure of chemical or mechanical energy is required. An electric current is accompanied by an electric field and a magnetic field. A device employed into determining the presence of an electric current is known as a galvanoscope. The conducting wire through which the electric current flows through is he led over and parallel to the galvanoscope the magnetoscope preset inside of the galvanoscope being deflected in the opposite direction to which the electric current flows in. So with the aid of a galvanoscope one may not only deduce the magnetic properties of an electric current, the exhibition of a magnetic field, but the direction in which the current flows through. An electromotive force may also be generators by a dynamo. A rotating magnet present inside of a helix. The magnetic properties of electric currents may be used to construct magnets. An electromagnet is commonly described as a mass of iron on which is placed a helix/solenoid through which flows an electric current. The magnetic field emitted by the electric current is increased if the solenoid is placed around a magnetic mass of iron or any other substance possessing magnetic properties, that is the magnetic field of the iron is added to that of the electric current producing a more powerful magnetic field. Conductors may be arranged in two variants. Series and parallel circuits. In series, the current passes through each conductor in turn, where Ohm's law changes to I = nE/(nr + R), where I is the current intensity, n is the number of cells arranged in series in the circuit, E is the electromotive force applied to the circuit, r is the internal resistance ( the resistance the current that is produced in the cell experiences whence passing from the zinc plate to the copper or carbon plate through the sulphuric acid ) and R is the external resistance.

For a good introduction to Gauss' Law and Ampere's Law, check out this website