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She is also married to Evelyn de Rothschild, whose estimated net worth is $20 billion. The main source of her income is E.L Rothchild, which is a holding company, and also she has sold her stakes in many companies in the past.

Sir Evelyn serves as Queen Elizabeth II's financial adviser. He has been a Governor of the London School of Economics and Political Science as well as an active patron of the arts and supporter of a number of charities. He served as Chairman of the Delegacy of St Mary's Hospital Medical School from 1977 to 1988.

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Typical polar radiation plot.

Since electromagnetic radiation is dipole radiation, it is not possible to build an antenna that radiates coherently equally in all directions, although such a hypothetical isotropic antenna is used as a reference to calculate antenna gain.

The simplest antennas, monopole and dipole antennas, consist of one or two straight metal rods along a common axis. These axially symmetric antennas have radiation patterns with a similar symmetry, called omnidirectional patterns; they radiate equal power in all directions perpendicular to the antenna, with the power varying only with the angle to the axis, dropping off to zero on the antenna's axis. This illustrates the general principle that if the shape of an antenna is symmetrical, its radiation pattern will have the same symmetry.

In most antennas, the radiation from the different parts of the antenna interferes at some angles; the radiation pattern of the antenna can be considered an interference pattern.

This results in zero radiation at certain angles where the radio waves from the different parts arrive out of phase, and local maxima of radiation at other angles where the radio waves arrive in phase. Therefore, the radiation plot of most antennas shows a pattern of maxima called "lobes" at various angles, separated by "nulls" at which the radiation goes to zero. The larger the antenna is compared to a wavelength, the more lobes there will be.

A rectangular radiation plot, an alternative presentation method to a polar plot.

For a complete proof, see the reciprocity (electromagnetism) article. 😉

Here, we present a common simple proof limited to the approximation of two antennas separated by a large distance compared to the size of the antenna, in a homogeneous medium.