The Magnetron Valve
The magnetron valve consists of a cylindrical anode surrounding a wire cathode. A solenoid is placed around the anode as shown below.
With no current in the coul the electrons travel straight from the cathod to the anode. As the current is increased, the electrons expereince a force perpendicular to the magnetic field (vertically upwards above). This force makes them follow a curved path. If the current (and so the field) is increased, a point will be reached at which the electrons just fail to reach the cathode. They follow the path indicated below.
For a field of flux densityfor the electrons to travel in a circle of radiuswe have(1)
The kinetic energy of the electron is equal toand this is equal to the potential energy gained,whereis the voltage difference between anode and cathode, so(2)
Cancel e/m from both sides to givethenIf the radius of the anode is R then
The value for the electrons to travel in a circle can be found because this is the value of the filed at which electrons will just fail to reach the anode, so the current between cathode and anode will just fall to zero.