Michael Faraday developed the idea of the electric field as lines of constant electric force radiating everywhere throughout space (known as the field theory).
Charles Augustine Coulomb:
F(e) = K(e) (q1q2/r^2) r^
where the electric force is inversely proportional to the square of the distance between two charges.
The Universal Law of Gravitation also follows a similar principle where F(g) = -G (m1m2/r^2)r^. This law led to the development of the theory and phrase "action at a distance" where bodies such as the earth and sun directly apply force to one another over copius kilometers.
F(e) = K(e) (q1q2/r^2) r^
F(g) = -G (m1m2/r^2)r^
F(m) = K(m) (p1p2/r^2)r^
All these laws have a force that decreases with the square of the distance.
The inverse square law is related to a simple geometric characteristic of space, known as flux, where intensity alpha = 1/r^2 describing the radiating light of the sun.
Faraday set out to solve the scientific mystery of why a compass needle spins to a perpendicular position from an electric charge, and developed an electric motor.
Anywhere in the vacinity of an electric charge a small test charge experiences a force. If it is due to only one charge the pattern of forces detected by the test charge is simple where similar forces repel and opposite forces attract.
The pattern of forces is present in a space as a field and can be expressed mathematically
F = sum (K(e) (qqi/ri^2) r^i)
The force that acts on a test charge at each point in space is equal to the test charge times a quantity of the other charges. That quantity is the electric field F = qE E= sum (K(e) (qqi/ri^2) r^i)
The 1/r^2 force between electric charges suggest that the force must be applied by something radiating outward from charges, something which like light from the sun never stops and never ends in space. These forces take characteristics of lines that never cross or angle. This electric field force is stronger near charges where lines (vectors) are close together and weak where the lines are far apart.
Gauss developed the mathematics of the Electric field theory through Gauss's Law:
for any closed surface total flux is proportional to the net electric charge inside. If there's no net charge inside a surface, any positive flux outward through it, must be balanced by inward, negative flux.
This law applies to light, gravitational fields, magnetic fields, and electric fields.
An electric field passing through a conductor forces the electrons to flow until they pile up at the surface repelling further motion of electron. The electric fiel inside any conductor becomes equal to zero when electrostatic equilibrium is established. Therefore, a closed surface inside the conductor has no flux through it, so the net charge inside must be zero, bu there can be charge at the surface. No matter what is outside, the surface charge makes the electric field inside equal to zero.
A metal box of any kind can keep out an electric field, known as the Faraday cage. This explains why drivers lose radio reception when passing through tunnels or bridges.
Gauss's law proves the theory of the center of mass.
Maxwell worked to express the electric field in mathematical terms.
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