This is the common problem of a charged particle moving in a static electric and magnetic field.
In the inertial frame of reference, the equation of motion is (1):
We can find equations for an and see that the resulting motion is a circular orbit with a constant drift velocity .
Surely I should get the same answer if I solve the problem in a rotating frame of reference?
I know that (2):
If I use Eq. (1) as the LHS of Eq. (2), and choose , then I get (3):
How do I obtain a constant drift velocity (as mentioned before) from this? Have I used any formula incorrectly? Does the electric field E= change form in the rotating frame?