My textbook says:
"Neils Bohr objected to the idea of an electron orbiting a nucleus in a circular orbit. An electron experiences centripetal acceleration and an accelerated charge radiates away energy. So such an orbit would be unstable: the electron would spiral into the nucleus."
But why does a charge radiate away energy when accelerated? From my understanding of circular motion, if the electron is in circular motion, then the centripetal force that is acting on the electron only changes the electron's direction and not its linear velocity. And hence the electron's kinetic energy should remain constant.
Therefore, if the energy that the charge radiates shouldn't come from the kinetic energy then what type of energy would it radiate away when accelerated and why? Thanks.
Answer
It emits light, because it "stirs up" the electromagnetic field. To understand this, just dip your finger into a still pond and move it in a circle. Water waves will emanate from your finger. These waves have energy, which means energy is being taken away from you. Same goes for the charges.
In fact, this follows almost automatically from the finite propagation speed of light. The electric field of a stationary charge obeys Coulomb's law. If the charge suddenly starts moving, the field won't obey Coulomb's law anymore, but it can't instantly change everywhere because of the finite propagation speed. Instead a "shockwave" of information goes out from the charge at speed $c$. This shockwave contains electromagnetic energy and travels at the speed of light -- it is light.
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