# Cyclotron motion

We know in a cyclotron motion, qvB=mv^2/R
Can you please tell me if the charge requires energy as it moves...
It is obvious that when it starts it requires energy provided by only the magnetic field. As it starts, it has constant velocity...no dissipation.Does it mean its energy remains constant?Then is Lorentz force is conservative?

Meir Achuz
Homework Helper
Gold Member
The B field does no work on a moving charge.
The particle would circle at constant speed and energy if radiation is neglected.

If B field does not do any work,how the charge sets into motion?

jtbell
Mentor
If B field does not do any work,how the charge sets into motion?
One must set the charge in motion by some means other than the B field. For example, one can accelerate the charges along a straignt line in an electric field and then "inject" the beam into the B field.

Or, while the charges are circulating in the B field, they can pass through short accelerating segments that produce an electric field. As the particles gain momentum, one increases the B field in step so as to keep the radius of the orbit constant. A modern large ring-accelerator like the ones at CERN and Fermilab has alternating accelerating and bending segments.