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# Field strength

In physics the '''field strength''' of a vector field|field is its Force (physics)|force per unit mass or charge at a point

## Gravitational field strength

The gravitational field field strength EG 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:
$E_G = frac\left\{F\right\}\left\{m\right\}$

Gravitational field strength has units N kg-1 The magnitude of gravitational field field strength can be calculated using Newton's law of universal gravitation:
$F = G frac\left\{M m\right\}\left\{r^2\right\}$

For a mass m the gravitational force acting on it equals: mEG So
$G frac\left\{M m\right\}\left\{r^2\right\} = mE_G$

Cancelling m gives:
$E_G = G frac\left\{M\right\}\left\{r^2\right\} = 4 pi G frac\left\{M\right\}\left\{4 pi r^2\right\}$

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 inside a uniform sphere increases linearly from its centre to its radius and from the surface decreases proportionate to the square of the distance from its centreearth This is because the gravitational flux density $frac\left\{M\right\}\left\{4 pi r^2\right\}$ decreases in proportion to the square of distance Also because the acceleration of a free falling body is equal to: F/m and g (the gravitational field field strength near the earth's surface) is also equal to F/m acceleration equals the field strength acting on it, g = a
The gravitational acceleration of the Earth is highest at the core mantle boundary at a depth of 2900 km: ca. $107 m/s^2$ It remains ca. $10 m/s^2$ until it increases to this maximum near this boundary then decreases approximately linearly to zero at the center([1] pdf)

## Electric field strength

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 electric field field strength at that point is defined as:
$E = frac\left\{F\right\}\left\{q\right\}$

The electric field field strength at a distance r can be calculated using
$F = frac\left\{1\right\}\left\{4 pi epsilon_0\right\} frac\left\{Qq\right\}\left\{r^2\right\}$

$E = frac\left\{F\right\}\left\{q\right\} = frac\left\{Q\right\}\left\{4 pi epsilon_0 r^2\right\}$

So
$E = frac\left\{Q\right\}\left\{4 pi epsilon_0 r^2\right\} = frac\left\{1\right\}\left\{epsilon_0\right\} frac\left\{Q\right\}\left\{4 pi r^2\right\}$

Where $epsilon_0$ represents permittivity of free space Note that here also the field intensity is proportional to the flux density $frac\left\{Q\right\}\left\{4 pi r^2\right\}$
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