Field strength in free space is a term in telecommunications. It is the field strength caused by a half wave dipole under ideal conditions. The actual field strength in terrestrial environments is calculated by empirical formulas based on this field strength.
Power density
Let N be the effective power radiated from an isotropic antenna and p be the power density at a distance d from this source^{[1]}
 $\backslash mbox\{p\}\; =\; \backslash frac\{N\}\{4\backslash cdot\; \backslash pi\; \backslash cdot\; d^2\}$
Power density is also defined in terms of electrical field strength;
Let E be the electrical field and R be the impedance of the free space
 $\backslash mbox\{p\}\; =\; \backslash frac\{E^2\}\{R\}$
The following relation is obtained by equating the two,
 $\backslash frac\{N\}\{4\backslash cdot\; \backslash pi\; \backslash cdot\; d^2\}=\; \backslash frac\{E^2\}\{R\}$
or by rearranging the terms
 $\backslash mbox\{E\}\; =\backslash frac\{\backslash sqrt\{N\}\; \backslash cdot\backslash sqrt\{R\}\}\{2\backslash cdot\; \backslash sqrt\{\backslash pi\}\backslash cdot\; d\}$
Numerical values
Impedance of free space is $120\; \backslash cdot\; \backslash pi$
Since a half wave dipole is used, its gain over an isotropic antenna ($\backslash mbox\{2.15\; dBi\}\; =\; 1.64$ ) should also be taken into consideration,
 $\backslash mbox\{E\}\; =\backslash frac\{\backslash sqrt\{1.64\; \backslash cdot\; N\}\; \backslash cdot\; \backslash sqrt\{\; 120\backslash cdot\; \backslash pi\}\}\{2\backslash cdot\; \backslash sqrt\{\backslash pi\}\backslash cdot\; d\}$
\approx 7\cdot\frac{ \sqrt{N}}{d}
In this equation SI units are used.
Expressing the same equation in:
 kW instead of W in power,
 km instead of m in distance and
 mV/m instead of V/m
is equivalent to multiplying the expression on the right by $\backslash sqrt\{1000\}$.^{[2]} In this case,
 $\backslash mbox\{E\}\; \backslash approx\; 222\backslash cdot\backslash frac\{\backslash sqrt\{N\}\}\{d\}$

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