Field strength

The gravitational field strength, E_G, at a point is the force per unit mass acting on a body arising from another object's mass. When a force acts on a point m, by definition:

E_G = F/m

Gravitational field strength has units N kg^-1. The magnitude of gravitational field strength can be calculated using Newton's law of gravitation: F = GmM/r². For a mass m, the gravitational force acting on it equals: mE_G. So,

GmM/r² = mE_G

Cancelling m gives:

E_G = GM/r²

Where r is the radius from the body's centre. Where the field originates from a sphere it can be assumed that the force acts from a point at its centre. The field strength of the earth increases linearly from its centre to its radius, and from the surface decreases proportionate to the inverse square of the distance from its centre. Also, because the acceleration of a free falling body is equal to: F/m, and g (the gravitational field strength near the earth's surface) is also equal to F/m, acceleration equals the field strength acting on it, g = a.

The electric field strength, E, is the force per unit charge a body exerts on another, much smaller, body. When a body of charge Q has a force F acting on it as a result of the field, the gravitational field strength at that point is defined as:

E = F/Q

The electric field strength at a distance r can be calculated using F = 1/(4(pi)e₀) * Qq/r².

E = F/q = Q/(4(pi)e₀r²)

So,

E = Q/(4(pi)e'r²)

Where e represents permittivity and e₀ permittivity of a free space.

The field strength of an electromagnetic wave is usually expressed as the rms value of the electric field, in volts per meter. The field strength of a magnetic field is usually expressed in ampere-turns per meter or in oersteds. Synonym radio field intensity[?].