Minimum Potential Difference Required

AI Thread Summary
The discussion revolves around determining the minimum potential difference required for electrons to reach the anode in a magnetron setup. Key concepts include the relationship between potential energy (PE) and kinetic energy (KE), with the total KE being the sum of radial and tangential components. The challenge lies in accounting for forces from both electric and magnetic fields, necessitating the formulation of differential equations to describe electron motion. There is uncertainty about applying conservation of energy due to the magnetic field's influence on electron trajectories. Overall, the problem requires a thorough analysis of forces and energy transformations in the system.
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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')
 
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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.
 
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