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Field strength

In physics, the field strength of a field is its force per unit mass or charge at a point.

Gravitational 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:

$E_G = \frac{F}{m}$

Gravitational field strength has units N kg^-1. The magnitude of gravitational 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 centre.earth 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 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 largest at the core-mantle boundary at a depth of 2900 km: ca. 10.7 m/s². Going downward from the surface, it remains ca. 10 m/s² until it increases to this maximum near this boundary, then decreases approximately linearly to zero at the center.([1] http://www.geo.cornell.edu/geology/classes/isacks/velstruct.pdf , 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 strength at that point is defined as:

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

The electric 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 $ε 0$ 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.

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Field strength

Gravitational field strength

Electric field strength

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