A magnetron creates electromagnetic waves from electrons. The electrons spiral,

Question

A magnetron creates electromagnetic waves from electrons. The electrons spiral, due to electric and magnetic fields, and end up in a circular orbit with a frequency of 2.4 GHz. The electrons pass through resonant chambers that result in microwaves, also with a frequency of 2.4 GHz. This is the heart of many microwave ovens! (a) What magnetic field strength is necessary to produce the desired orbit frequency? (b) The magnetron is cylindrical, and has a diameter of 2.5 cm. What is the maximum possible kinetic energy of the electrons, before they hit the wall?

Explanation / Answer

centrifugal force on electron = force due to magnetic field
mv²/r = qvB

Since v = r,
m²r = qrB
m = qB
B = m/q
B = (9.11e-31 kg)(2.4e9 s^-1)(2) / (1.60e-19 C)
B = 8.6e-2 T (86 mT)

b)
K = (1/2)mv²
K = (1/2)m²r²
K = (1/2)(9.11e-31 kg)[(2.4e9 s^-1)(2)]²(2.5e-2 m / 2)²
K = 1.6e-14 J (16 fJ)

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