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SpyIntel [72]
3 years ago
7

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 strength of the magnetic field?
Physics
1 answer:
Rama09 [41]3 years ago
7 0

Answer:

<em>The magnetic field is 0.0857 T.</em>

Explanation:

The electrons orbit the magnetic field with a centripetal force equal to

F = \frac{mv^{2} }{r}

also, the force on an electron in a magnetic field is gotten as

F = Bqv

equating this two equations give

\frac{mv^{2} }{r} = Bqv

mv/r = Bq

where m is the mass of the electron = 9.11 x 10^-31 kg

v is the the linear speed of the electron

B is the magnetic field on the electron

r is the radius of the orbital movement

q is the charge on an electron = 1.602 x 10^-19 C

but, the linear speed v = ωr

where ω is the angular speed of the electron

substituting into equation above, we have

mωr/r = Bq

which reduces to

mω = Bq

finally, w know that the angular speed is related to the frequency of the electron by

ω = 2πf

we then finally have

2mπf = Bq

where f is the frequency emitted by the electron = 2.4 GHz = 2.4 x 10^9 Hz

substituting values into the equation, we have

2 x 9.11 x 10^-31 x 3.142 x 2.4 x 10^9 = B x 1.602 x 10^-19

B = (1.3734 x 10^-20)/(1.602 x 10^-19) = <em>0.0857 T</em>

= <em>85.7 mT</em>

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