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 *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:

- $E\_G\; =\; frac\{F\}\{m\}$

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**:

- $F\; =\; G\; frac\{M\; m\}\{r^2\}$

For a

mass *m* the gravitational

force acting on it equals:

*mE*_{G} So

- $G\; frac\{M\; m\}\{r^2\}\; =\; mE\_G$

Cancelling

*m* gives:

- $E\_G\; =\; G\; frac\{M\}\{r^2\}\; =\; 4\; pi\; G\; frac\{M\}\{4\; pi\; r^2\}$

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 $frac\{M\}\{4\; pi\; r^2\}$ 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:

- $E\; =\; frac\{F\}\{q\}$

The

electric field field strength at a

distance *r* can be calculated using

- $F\; =\; frac\{1\}\{4\; pi\; epsilon\_0\}\; frac\{Qq\}\{r^2\}$

- $E\; =\; frac\{F\}\{q\}\; =\; frac\{Q\}\{4\; pi\; epsilon\_0\; r^2\}$

So

- $E\; =\; frac\{Q\}\{4\; pi\; epsilon\_0\; r^2\}\; =\; frac\{1\}\{epsilon\_0\}\; frac\{Q\}\{4\; pi\; r^2\}$

Where

$epsilon\_0$ represents

permittivity of

free space Note that here also the field intensity is proportional to the

flux density $frac\{Q\}\{4\; pi\; r^2\}$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**## See also