The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at , and as they do so they emit electro-magnetic 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 , what is the maximum electron kinetic energy?
a)The strength of the magnetic field is
b)The maximum electron kinetic energy is
The given is the circular frequency and the diameter of the chamber is . The objective is to find the magnetic field strength and energy.
a) The magnetron motion is the uniform circular motion of a particulate perpendicular to the magnetic field at a constant speed. The magnetic field causes the circular motion to produce a circular frequency, which is given by an equation in the form
Where is the particle's charge, is the magnetic field, and is the particle's mass. The frequency is determined by the magnetic field rather than the particle's velocity, as indicated by the equation. For , we rearrange the equation so that it looks like this:
Now, we plug the values for , and of the electron to get
b) The radius of the circular motion produced by the magnetic field is related to it by an equation in the form
The diameter of the chamber is , so we get the radius by
We rearrange the equation for the speed and plug the values for to get the speed of the electron
The kinetic energy is half the product of the mass and the velocity square
Now, we plug the values for and into the equation to get of the electron
FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to “float” so as to form an equilateral triangle with the lower wires?
The coaxial cable shown in consists of a solid inner conductor of radius surrounded by a hollow, very thin outer conductor of radius . The two carry equal currents I, but in opposite directions. The current density is uniformly distributed over each conductor.
a. Find expressions for three magnetic fields: within the inner conductor, in the space between the conductors, and outside the outer conductor.
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