Dipole field strength in free space
# Dipole field strength in free space

Dipole field strength in free space, in telecommunications, is the electric 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

    ${\mbox{p}}={\frac {N}{4\cdot \pi \cdot d^{2}}}$

Power density is also defined in terms of electrical field strength;

Let E be the electrical field and Z be the impedance of the free space

    ${\mbox{p}}={\frac {E^{2}}{Z}}$

The following relation is obtained by equating the two,

    ${\frac {N}{4\cdot \pi \cdot d^{2}}}={\frac {E^{2}}{Z}}$

or by rearranging the terms

    ${\mbox{E}}={\frac {{\sqrt {N}}\cdot {\sqrt {Z}}}{2\cdot {\sqrt {\pi }}\cdot d}}$

## Numerical values

Impedance of free space is roughly $120\cdot \pi$

Since a half wave dipole is used, its gain over an isotropic antenna (${\mbox{2.15 dBi}}=1.64$ ) should also be taken into consideration,

    ${\mbox{E}}={\frac {{\sqrt {1.64\cdot N}}\cdot {\sqrt {120\cdot \pi }}}{2\cdot {\sqrt {\pi }}\cdot d}}\approx 7\cdot {\frac {\sqrt {N}}{d}}$

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 in electric field

is equivalent to multiplying the expression on the right by ${\sqrt {1000}}$. In this case,

    ${\mbox{E}}\approx 222\cdot {\frac {\sqrt {N}}{d}}$
