7. You are getting ready to make your lunch in the microwave (reheated dinner fr

Question

7. You are getting ready to make your lunch in the microwave (reheated dinner from the night before, yum). While it is running you start to think about how it works. You find out, using the internet, that the electrons orbit the magnetic field at 2.4Ghz, due to the magnetron, and as they due this the emit 2.4GHz electromagnetic waves (this is what heats your food). a) What is the B-field strength? b) If the max diameter the electron can have before it hits the side of the magnetron tube is 2.3cm, what is the max electron kinetic energy?

Explanation / Answer

Forces on electron

centripetal force = magnetic force

mv^2/ r = qVB

mv/r = qB

v = rqB/ m

T = 2pir / v

f = v/ 2pir = (  rqB/ m2pir) = ( qB/ 2pim)

B = ( f x 2 x pi x m / q) = ( 2.4 x 10^9 x 2 x 3,14 x 9.109 x 10^-31 / 1.6 x 10^-19) = 8.58 x 10^-2 T or 86 mT apprx

b) let's find the velocity at the specified diameterm

v = ( 1.15 x 10^-2 x1.6 x 10^-19 x 8.58 x 10^-2 / 9.109 x 10^-31)

v =1.733 x 10^ 10 m/s

KE = 0.5 ( 9.109 x 10^-31) ( 1.733 x 10^ 10 m/s)^2= 13.68 x 10^ -11 J

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