Field strength and energy of electrons in a magnetron

[mrroboto]

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

 

[Mentz114]

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.

 

[Moetasim]

.

I would like to clarify and expand upon the information provided in the question. A magnetron is a type of vacuum tube used in microwave ovens to generate high-frequency electromagnetic waves. It works by using a strong magnetic field to guide electrons in circular orbits, causing them to emit microwaves as they accelerate.

To answer part (a) of the question, the magnetic field strength in a magnetron can vary depending on the design and application, but it is typically in the range of 0.1-1 tesla (T). Using the equation provided, we can estimate the magnetic field strength for a 2.4 GHz frequency to be approximately 0.028 T.

Part (b) asks about the maximum kinetic energy of the electrons in the magnetron. This is a more complex question as it involves the dynamics of the electron orbits and the acceleration of the electrons by the magnetic field. The maximum diameter of the electron orbit before hitting the wall of the tube is a measure of the electron's gyroradius, which is dependent on the electron's mass, charge, and velocity. Without additional information about the design and operating conditions of the magnetron, it is difficult to accurately calculate the maximum kinetic energy of the electrons. However, it is safe to say that the electrons in a magnetron have a significant amount of kinetic energy due to their accelerated motion in a strong magnetic field. This energy is then converted into electromagnetic waves, which can be used for heating and cooking in a microwave oven.