# Do accelerated moving electrons radiate electromagnetic energy?

Do accelerated moving electrons radiate electromagnetic energy?

Generally speaking, the charge should absorb energy instead of radiating energy in the acceleration stage, and release energy in the deceleration stage. Acceleration is that charge absorbs external energy into kinetic energy, and deceleration is that kinetic energy is released in the form of electromagnetic radiation.

For example, let's look at X-ray machines. Do electrons radiate in the accelerating phase of an electric field? And look at the electrons in the linear accelerator. Do we need to pay attention to the difference in physics?

In classical electrodynamics, the power radiated by a non-relativistic point charge in vacuum is given by the Larmor formula. According to Larmor formula, a charge is radiating energy while changing speed. To clarify the difference, simple experiment works. Using electronic fields, let charges be accelerated then decelerated, detect the radiation at the two phases and compare them.

In linear electron accelerator, do the electrons radiate while speeding up? They do radiate while being slowed down(bremsstrahlung).

We do not say bad and disputed word of acceleration or deceleration, just ask do charges release energy while gaining energy? kinetically or potentially. Electron transition doesn't. It emits photon only when it is releasing potential energy.

In terms of the standard textbook answer, Larmor's formula is derived based on the electric field of an charge in vacuum with acceleration. When the charge is accelerated by an outside electric field, this derivation may not be applicable. Because there is a stronger electric field and interaction with the charge. At least the flux line shown in the derivation is not there or not of that shape, which is changed by the bending of the external electric field. Moreover, this formula is not suitable for charge radiation in atoms.

• There is no "deceleration" in physics. Acceleration is a vector quantity. "Deceleration" is how a lay-person describes the situation when the acceleration of a body points in approximately the opposite direction to its velocity. Jul 21, 2019 at 0:09
• The X generator uses high-speed electrons accelerated by an electric field to bombard large-mass materials. The electrons are slowed down and the original kinetic energy is released. Jul 21, 2019 at 0:19
• Re, "the electrons are slowed down..." My point is, when something slows down, a lay-person might call it "deceleration," but a physicist calls it "acceleration." The only way that the velocity of an object with mass (e.g., an electron) can change, is if a force acts on it. It's the same phenomenon regardless of whether the force acts to speed the object up in some frame of reference or, to slow it down. Jul 21, 2019 at 0:28
• @SolomonSlow One could argue that an adequate definition of deceleration is an acceleration that decreases the speed of the object. Although I agree that the distinction is never really useful in physics. Jul 21, 2019 at 2:06
• @AaronStevens That way lies pedagogical disaster. Students will think that if deceleration leads to decreased speed, acceleration leads to increased speed. Jul 21, 2019 at 5:48

## 1 Answer

In classical electrodynamics, the power radiated by a non-relativistic point charge in vacuum is given by the Larmor formula:

$$P = \frac{\mu_0 q^2 a^2}{6 \pi c}$$ where $$q$$ is the charge, $$a$$ is the magnitude of the acceleration, $$\mu_0$$ is the permeability of free space and $$c$$ is the speed of light. Thus the power does not depend on the direction of acceleration, only the magnitude; and an accelerating charge always radiates power regardless of whether it is slowing down ("decelerating"), speeding up, or neither.