Field strength and energy of electrons in a magnetron

AI Thread Summary
The discussion focuses on calculating the magnetic field strength and maximum kinetic energy of electrons in a magnetron, which produces microwaves at 2.4 GHz. The magnetic field strength can be determined using the formula frequency = qB/2(pi)m by substituting the known values for charge, frequency, and mass of the electron. For part (b), the tangential velocity of the electron is calculated based on its circular motion with a diameter of 2.5 cm, using the angular velocity derived from the frequency. This velocity is then used to compute the maximum kinetic energy of the electron. Understanding these calculations is essential for grasping the operation of magnetrons in microwave ovens.
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Homework Statement



The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at 2.4 GHz, and as they do so they emit 2.4 GHz electromagnetic waves.

a) what is the magnetic field strength?
b) if the maximum diameter of the electron orbit before the electron hits the wall of the tube is 2.5 cm, what is the maximum electron kinetic energy?


Homework Equations



frequency = qB/2(pi)m

The Attempt at a Solution



2.4 GHz = (1.6 x 10^-19)(B)/ 2(pi)(9.109 x 10-31)

then solve for B. is that right?

I don't understand part (b) at all
 
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Well, yes, the first part is just plugging in numbers and calculating.

The second part requires you to calculate the tangential velocity of an electron moving in a circle of diameter 2.5 cm with an angular velocity omega = 2*Pi*2.4 GHz. Given that you can work out the KE.
 
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