Behaviour of free electron with constant velocity Can a free electron with a constant velocity V то move eternally at this rate in the inertial frame? The question arises from the fact that a moving charge creates near its trajectory varying electric and magnetic fields. Whether kinetic energy of electron is spent for it?  
 A: There's a very easy way to see that an electron moving at constant velocity does not slow down.
Suppose we consider a stationary electron and an uncharged particle like a neutron moving at some velocity $v$. Obviously the neutron can't radiate EM energy, so the relative velocity will remain $v$ indefinitely.
Now suppose you're in a spaceship moving at velocity $v$. When you look out of your window you see a stationary neutron and an electron moving at $-v$, and because the relative velocity does't change the velocity of the electron remains at $-v$ indefinitely.
But there are no absolute velocities - the frame in which the neutron is stationary and the electron is moving obeys the same physical laws as the frame in which the electron is stationary and the neutron is moving. That means an electron moving at a constant speed in any frame cannot lose energy and slow down.
Note that the argument doesn't apply to accelerated motion because (in SR at least) acceleration isn't relative. You can always identify whether it's the electrion or neutron accelerating. That means accelerated electrons can, and indeed do, radiate EM energy and slow down.
