Minimum Potential Difference Required

[E&M]

Homework Statement

Consider a magnetron. It consists of an electron-emitting filament at the center of a cylindrical anode situated in a uniform magnetic field. Electrons of charge e and mass m are emitted with negligible velocity from the filament.

What is the minimum potential difference between the filament and anode for elctrons to reach the anode.

Homework Equations

PE = KE

F = d (mv)/dt

The Attempt at a Solution

total kinetic energy of the electron = radial KE + Tangential KE
Total KE = PE of the electron (i.e. 'eV')

 

[Redbelly98]

I'm not sure, but it looks like you'll need to write out expressions for the force (due to electric and magnetic fields), and solve the differential equation for the electron's motion. This does not look trivial.

Not sure if conservation-of-energy can be applied here, since the magnetic field causes the electron paths to curve.