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Time period or frequency of a charged particle's circular motion in a field

This type of question, asked 3 times: 25 Jul 2022, 24 Jan 2025, 4 Apr 2025. All 3 questions below, oldest first.

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  1. Question 1

    25 Jul 2022

    101
    An electron with energy 0.1keV0.1keV moves at right angle to the earth's magnetic field of 1×10−4Wbm−21 \times10^{- 4}Wbm^{- 2}. The frequency of revolution of the electron will be (Take mass of electron =9.0×10−31 kg= 9.0 \times10^{- 31}\text{ }kg )

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  2. Question 2

    24 Jan 2025

    96
    A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is _______\_\_\_\_\_\_\_ . [Take mass of electron m0=9×10−31 kgm_{0}= 9 \times10^{- 31}\text{ }kg, charge of electron ∣q0∣=1.6×10−19C\left| q_{0} \right|= 1.6 \times10^{- 19}C,  μ0=4π×10−7 N A2,1 ns=10−9 s]\left. \ \mu_{0}= 4\pi\times10^{- 7}\frac{\text{ }N}{{\text{ }A}^{2}},1\text{ }ns =10^{- 9}\text{ }s \right\rbrack

  3. Question 3

    4 Apr 2025

    96
    A particle of charge 1.6μC1.6\mu C and mass 16μ g16\mu\text{ }g is present in a strong magnetic field of 6.28 T . The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ____\_\_\_\_ ms. ( π=3.14\pi = 3.14 )