Dipole field strength in free space

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

p = N 4 ⋅ π ⋅ 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

p = E 2 R

The following relation is obtained by equating the two,

N 4 ⋅ π ⋅ d 2 = E 2 R

or by rearranging the terms

E = N ⋅ R 2 ⋅ π ⋅ d

Numerical values

Impedance of free space is roughly 120 ⋅ π

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

E = 1.64 ⋅ N ⋅ 120 ⋅ π 2 ⋅ π ⋅ d ≈ 7 ⋅ 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 1000 . In this case,

E ≈ 222 ⋅ N d