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electric monopoles cannot radiate?

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According to a physics gre book (Conquering Physics GRE by Kahn &Anderson), electric 'monopoles do not radiate'. They give the example that a uniformly charged sphere can change radius and not radiate...I understand this, but what about just a point charge? Surely it can radiate when accelerated(for example, synchrotron radiation). Should they instead have said that "some" monopoles cannot radiate? Does this mean that "all" accelerating electric dipoles radiate? Any help in understanding this is appreciated! :)

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