In the third edition of Griffith's Introduction to Electrodynamics, in section 11.1.4, he says that an electric monopole does not radiate because the electric charge is conserved. But we do know that a point charge radiates when it accelerates. What am I missing?
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But a point charge (electric monopole) does radiate. There are a Lienard-Wiechert fields that give rise to nonzero radiated power. – Solidification Dec 14 '22 at 04:46
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A moving point charge has higher order terms in the potential, higher than the monopole terms. – hft Dec 14 '22 at 05:14
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Griffiths is correct, and so are you. You just mean different things by the word "monopole".
You mean "monopole" as in "a point charge".
Griffiths means "monopole" as in "the leading term of the multipole expansion for an electric field".
Griffiths is correct that a time-dependent monopole contribution does not radiate. However, the field in your example has a dipole contribution due to the charge's motion (and perhaps even higher monopoles, I don't remember by heart right now), and hence it can indeed radiate.
Griffiths' statement could be restated as "there is no radiation in spherically-symmetric charge configurations" since the monopole contribution is the sole one that is spherically symmetric (all of the other ones come from spherical harmonics of the form $Y_l^m$ with $l \geq 1$). This is true since the only spherically-symmetric solution for the Maxwell equations in the absence of matter (which is the relevant case at the radiation region) is the Coulomb solution, which does not have radiation.
Níckolas Alves
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