Question

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.
What is the magnetic field strength?


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?

Answer 1

Answer:

The magnetic field strength is 0.086 T

The maximum kinetic energy is $1.62 \times 10^{-14}$ J

Explanation:

Given:

Frequency $f = 2.4 \times 10^{9}$ Hz

(A)

The magnetic field related to cyclotron is given by,

  $B = \frac{2\pi mf}{e}$

Where $m =$ mass of electron $= 9.1 \times 10^{-31 }$ kg, $e = 1.6 \times 10^{-19}$ C

  $B = \frac{6.28 \times 9.1 \times 10^{-31 }\times 2.4 \times 10^{9} }{1.6 \times 10^{-19} }$

 $B = 0.086$ T

Therefore, the magnetic field strength is 0.086 T

(B)

Diameter of orbit $d= 2.5 \times 10^{-2}$ m

Radius of orbit $r = 1.25 \times 10^{-2}$ m

The maximum kinetic energy is given by,

   KE = $\frac{1}{2} mv^{2}$

Where $v = r \omega = r 2\pi f$

   KE = $\frac{1}{2} m(2\pi fr)^{2}$

   KE = $\frac{1}{2} \times 9.1 \times 10^{-31 } \times (2 \times 3.14 \times 2.4 \times 10^{9} \times 1.25 \times 10^{-2} )^{2}$

   KE = $1.62 \times 10^{-14}$ J

Therefore, the maximum kinetic energy is $1.62 \times 10^{-14}$ J