# Radiation from accelerated charge

• azaharak

#### azaharak

If a charge undergoes acceleration it emits electromagnetic radiation.

Where does the energy associated with this radiation come from?

Thank you very much

## Answers and Replies

The charge recoils against the radiation and slows. Another way to look at it is that it is harder to accelerate a charged object than an equivalent neutral object.

If a charge undergoes acceleration it emits electromagnetic radiation.

Where does the energy associated with this radiation come from?

Thank you very much

Whatever has accelerated the charge has put energy into it to get it going. An external force does work, the charge gains kinetic energy, then gives off some of this kinetic energy as radiative energy and slows down in the process.

Think of a circular particle accelerator speeding up small bunches of protons along its circular track. Energy from the electrical power grid is transferred into the electromagnetic control fields used to accelerate the protons. The protons then emit some of that energy as radiation.

So then in undergradaute texts, when your given a proton in an external electric field, and asked to find the speed of the proton after some time t, technically you can not use kinematic equations and assume the acceleration will be the field times charge divided by mass, as it should be loosing some of its kinetic energy simultaneously as it is accelerating.

Obviously we shouldn't even tackle this with classical mechanics.

well the accelerating will be that from the field, but its speed will be affected by some other deceleration which accounts for the lost kinetic energy too