# Why there can't be an isotropic radiator?

Why there can't be an isotropic radiator? I know you can prove it using Maxwell's equations but I don't see how. Can someone please help?

• Have you read the Wikipedia article? If so, what is unclear about the proof? Commented Nov 15, 2022 at 19:50
• @Chemomechanics if one is asking about a proof in a mathematical sense then the wikipedia's argument is not quite a "proof" because the field is never exactly tangential to a sphere centered around the radiator, in fact it can never be completely tangential at any a finite distance as it can be seen from Ignatowski's equations. I am not saying that the argument is wrong, just that it is not quite complete. I think it needs some more extensive $\epsilon$ and $\delta$ argument in addition to the one usually provided. Commented Nov 15, 2022 at 20:21
• But more importantly the "hairy ball" theorem would only restrict a radiation pattern that is linearly polarized. Matzner and McDonald synthesized an elliptically polarized isotropic radiation that is not restricted by the "hairy ball" theorem and has a spherically uniform magnitude, which what is really expected from a spherically uniform radiator, see here doi.org/10.48550/arXiv.physics/0312023 Commented Nov 15, 2022 at 20:21
• now that @buzz deleted my perfectly correct answer and converted into a comment without any explanation it will soon disappear in cyberspace. Wow, buzarre bizz. Commented Nov 16, 2022 at 4:09
• @hyportnex: Your answer was written as a response to a comment, and wouldn't have made much sense without it if that comment had gone away. So I flagged it as "not an answer". If you rewrote the content of your answer so that it could stand on its own, with minimal reference to other comments, it would probably be fine. Commented Nov 16, 2022 at 12:49