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Question 12

 In Exercise, obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Answer

Magnetic field strength, B = 6.5 × 10 - 4 T

Charge of the electron, e = 1.6 × 10 - 19 C

Mass of the electron, me = 9.1 × 10 - 31 kg

Velocity of the electron, v = 4.8 × 106 m/s

Radius of the orbit, r = 4.2 cm = 0.042 m

Frequency of revolution of the electron = v

Angular frequency of the electron = w = 2πv

Velocity of the electron is related to the angular frequency as:

v = rw

In the circular orbit, the magnetic force on the electron is balanced by the centripetal force. Hence, we can write:

This expression for frequency is independent of the speed of the electron.

On substituting the known values in this expression, we get the frequency as:

Hence, the frequency of the electron is around 18 MHz and is independent of the speed of the electron.

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