Electromagnetic Field

An electromagnetic field is an area in which electric and magnetic forces are interacting. It arises from electric charges in motion. Electromagnetic fields are directly related to the strength and direction of the force that a charged particle, called the "test" charge, would be subject to under the electromagnetic force caused by another charged particle or group of particles, called the source.

An electromagnetic field is best understood as a mathematical function or property of spacetime, but may be represented as a group of vectors, arrows with specific length and direction. For a static electric field, meaning there is no motion of source charges, the force F→ on a test charge is F→ = qE→, where q is the value of the test charge and E→ is the vector electric field. For a static magnetic field (caused by moving charge inside an overall neutral group of charges, or a bar magnet, for example) the force is given by F→ = qv→ × B→, where v→ is the charge velocity, B→ is the vector magnetic field, and the × indicates a cross-product of vectors.

A stationary charge produces an electric field, while a moving charge additionally produces a magnetic field. Since velocity is a relative concept dependent on one's choice of reference frame, magnetism and electricity are not independent, but linked together, hence the term electromagnetism.

The field of a static point charge

According to Coulomb's law, the strength of the electric field from a nonmoving point charge depends directly on the charge value q and is inversely proportional to the distance from the charge. That is, farther from the source charge will be subject to the same strength of force regardless of whether it is above, below, or to the side of the source, as long as the distance is the same. A surface of the same radius all around the source will have the same field strength. This is called a surface of equipotential. For a point source charge, the surface of equipotential is a sphere, and the force F will push a positive charge radially outward. A test charge of mass m and positive charge q will feel a push away from the positive source charge with an acceleration (a) directly proportional to the field strength and inversely proportional to the mass of the test charge.

If a charge does not move because it is acted upon by the electromagnetic force equally from all directions, it is in a position of stable equilibrium.

Next, we consider the field due to a group of positive charges evenly distributed along an infinite straight line, defined to be infinite because we want to neglect the effect of the endpoints as an unnecessary complication here. Just as the field of a point charge is directed radially outward in a sphere, the field of a line of charge is directed radially outward, but at any specific radius the surface of equipotential will be a cylinder.