How Does a Rotating Charged Particle Beam Maintain Focus?

[jughead4466]

Particles having mass = m and charge = Q travel parallel to the z axis, forming a beam of radius = R and uniform charge density = p. To keep the beam focused, an external uniform electric field _{}Bo, parallel to the z axis is provided, and the beam is made to rotate with a constant, uniform angular velocity = w

A: Use Gauss' Law to find the radial electric field in the beam on a cylinder of radius = r<R

I figured out this one and got E = pr/2\epsilon

Sorry about the coding, I'm very new to this. Well that is supposed to be epsilon, and it should not be a power.

I could not figure out B or C though.

B: Find the azimuthal (tangential) velocity of a particle in the beam at r<R

C: Find the total (electric and magnetic) force required on a particle at r<R

D: Set force in "C" equal to the centripetal force required to keep a particle on a circular path of radius = r<R

 

[jughead4466]

edit. double post