Minimum Potential Difference Required

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SUMMARY

The discussion focuses on calculating the minimum potential difference required for electrons to reach the anode in a magnetron setup. It emphasizes the relationship between potential energy (PE) and kinetic energy (KE), specifically stating that the total kinetic energy of the electron is equal to the potential energy represented by 'eV'. The conversation highlights the necessity of deriving expressions for the forces acting on the electrons due to electric and magnetic fields, and solving the resulting differential equations to understand the electron's motion. The complexity of applying conservation of energy in this context is also noted due to the influence of the magnetic field on electron trajectories.

PREREQUISITES
  • Understanding of electron dynamics in electric and magnetic fields
  • Familiarity with potential energy and kinetic energy equations
  • Knowledge of differential equations and their application in physics
  • Basic principles of magnetron operation
NEXT STEPS
  • Study the derivation of force equations in electric and magnetic fields
  • Learn about the motion of charged particles in magnetic fields
  • Explore the application of conservation of energy in non-linear systems
  • Investigate the mathematical modeling of magnetron behavior
USEFUL FOR

Physics students, electrical engineers, and professionals involved in the design and analysis of magnetrons and similar electron devices.

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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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