Understanding Electric Fields and Coulomb's Law

A stationary charge emits an electric field which expands indefinitely throughout space and time continually getting weaker and weaker. The electric field is measured in Newton per Coulomb or Volts per meter. The direction of the electric field at a point in time and space is defined by the direction of the electric force exerted on a positive test charge placed at that point while the strength of the electric field is defined by the ratio between the electric force on a charge at a point and the magnitude of the charge placed at that point. A moving charge emits a magnetic field and is measured in the unit of Tesla (in honor of Nicola Tesla). The magnetic field will always be orthogonal (perpendicular) to the electric field and will always be going from a positive or north terminal to a negative or south terminal. The combination of these two fields produces the electromagnetic field which is what is most commonly used in today's technology to produce many of the amazing pieces of technology that we take for granted. A stationary point charge "a" of a specified charge Q1 will produce an electric field which will apply a force on another freely moving point charge "b" of a specified charge Q2. This force can be calculated using the following formula:

F12 = [(KQ1Q2)/r2]*R where K = 1/(4πε0), R is the unit vector between the two point charges and r is the distance in meters between the two point charges.

Depending on the sign of Q1 and Q2 (charges of the two point charges) the force being applied to the two point charges will be either an attractive or repulsive force. If "a" has a negative charge while "b" has a positive charge or if "a" has a positive charge while "b" has a positive charge, the force being applied to 'b" by "a" will be an attractive force because the resulting force will have a negative value. If the charge of "a" and "b" are both positive or both negative then the resulting force of "a" on "b" will be a repulsive force because the resulting force will have a positive value. Hence the general rule of how opposite attract was derived. The force of an electric field in general is calculated using the following formula:

F = Eq where E is the electric field and q is the charge of a test charge.

If more than one charge is present then the resulting electric field, at a certain point, is defined by the sum of all the electric fields presents with respect to their individual unit vectors (the unit vectors are with respect to the individual point charge and the specified point where the electric field is to be calculated). In other words, the vector sum of all the electric fields present and therefore the formula which expresses this is as follows:

Et = Σ E1 + E2 + ... En

With the above principle in mind, the electric field at a specified point derived from an infinite number of infinitesimally small elements of charge (usually taking the form of an abnormally shaped object which emits a non-uniform but continuous electric field) can be expressed as:

Et = K ∫ [ρ/r2]*R dV where ρ is the amount of charge per unit volume and r is the distance between the specified point and the infinite number of infinitesimally small elements of charge and R is the unit vector.