Electric field

 An electric field (sometimes abbreviated as E-field) is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge by an infinitesimal test charge at that point. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m).

Electric fields are created by electric charges, or by time-varying magnetic fields. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.

Electric Lines of Force:

An electric line of force is an imaginary continuous line or curve drawn in an electric field such that tangent to it at any point gives the direction of the electric force at that point. The direction of a line of force is the direction along which a small free positive charge will move along the line. Field lines directed into a closed surface are considered negative; those directed out of a closed surface are positive. If there is no net charge within a closed surface, every field line directed into the surface continues through the interior and is directed outward elsewhere on the surface.

Electric Flux:

Electric flux is a property of an electric field that may be thought of as the number of electric lines of force (or electric field lines) that intersect a given area. Electric field lines are considered to originate on positive electric charges and to terminate on negative charges. If a net charge is contained inside a closed surface, the total flux through the surface is proportional to the enclosed charge, positive if it is positive, negative if it is negative.

The mathematical relation between electric flux and enclosed charge is known as Gaussfs law for the electric field, one of the fundamental laws of electromagnetism.

Where E is the electric field (having units of V/m), E is its magnitude, S is the area of the surface, and .. is the angle between the electric field lines and the normal (perpendicular) to S.

For a non-uniform electric field, the electric flux dƒ³E through a small surface area dS is given by