Good morning. I was wondering which is the exact physical reason for why a dipole (e.g. a $\lambda/2$ dipole) has the equal radiation pattern in all directions. I have founded many formulas but I can't get the point in practice. Many thanks.
in free space, a dipole is not isotropic: it radiates in a fat "figure-8" pattern with two lobes. the "null point" where the radiation goes to nearly zero corresponds to the direction along the length of the dipole i.e., very little energy is radiated away from the ends of the dipole.
As a dipole antenna is moved close to the ground, its radiation pattern becomes distorted by currents it sets up in the ground and then the radiation pattern becomes less lobe-like and more isotropic.