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Question

In Exercise 4.11 obtain the frequency of revolution of the electron inits circular orbit. Does the answer depend on the speed of the electron? Explain.


Solution

Given: The magnetic field strength is 6.5× 10 4 T, the charge of the electron 1.6× 10 19 C, the velocity of the electron is 4.8× 10 6 m/s, the radius of the orbit is 4.2cm, the mass of the electron is 9.1× 10 31 kg.

The velocity of the electron is given as,

υ=rω

Where, the angular frequency is ω and the radius of the orbit is r.

The angular frequency of the electron is given as,

ω=2πν

Where, the frequency of revolution of the electron is ν.

Since, in the circular orbit, centripetal force balances the magnetic force on the electron in the circular orbit.

The balance of these forces is given as,

m υ 2 r =eυB

Further simplifying the above expression, we get

eB= mυ r eB= m( ωr ) r ν= eB 2πm

Where, the magnetic field strength is B, the charge of the electron is e and the mass of the electron is m.

By substituting the given values in the above expression, we get

ν= 6.5× 10 4 ×1.6× 10 19 2×3.14×9.1× 10 31 =18.2× 10 6 Hz =18.2MHz

Thus, the frequency of the electron is 18.2MHzand it is independent of the speed of the electron.


Physics
Physics Part-I - NCERT
Standard XII

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