The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit in a magnetic field of 9.6 x 10^-2 T at a frequency of 2.7 GHz, and as they do so they emit 2.7 GHz electromagnetic waves.

a) 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 velocity the electrons may have?

Question

Physics

Ansley

20 February, 23:11

The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit in a magnetic field of 9.6 x 10^-2 T at a frequency of 2.7 GHz, and as they do so they emit 2.7 GHz electromagnetic waves.

a) 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 velocity the electrons may have?

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Answers (1)

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Frosty · Answer 1

For equilibrium of rotating electron in outermost circular path

Centripetal force = force on electron

m v² / r = B q v

v = B q r / m, v is velocity of electron, B is magnetic field, q is charge on electron, r is radius of circular path.

v = 9.6 x 10⁻² x 1.6 x 10⁻¹⁹ x 1.25 x 10⁻² / 9.1 x 10⁻³¹

= 2.1 x 10⁸ m / s