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Charged particle moving in a circle around a long line charge or charged cylinder: speed, kinetic energy or period

This type of question, asked 4 times: 14 Jun 2022, 10 Apr 2023, 30 Jan 2024, 4 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    106
    A long cylindrical volume contains a uniformly distributed charge of density ρ\rho. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is:

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  2. Question 2

    10 Apr 2023

    120
    An electron revolves around an infinite cylindrical wire having uniform linear charge density 2×10−8Cm−12 \times10^{- 8}Cm^{- 1} in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is____ ×106 ms−1\times10^{6}{\text{ }ms}^{- 1}. Given mass of electron =9×10−31 kg= 9 \times10^{- 31}\text{ }kg.
  3. Question 3

    30 Jan 2024

    103
    A particle of charge ' −q-q ' and mass ' mm ' moves in a circle of radius ' rr ' around an infinitely long line charge of linear density ' +λ+\lambda '. Then time period will be given as: (Consider k as Coulomb's constant)

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  4. Question 4

    4 Apr 2024

    16
    An infinitely long positively charged straight thread has a linear charge density λCm−1\lambda Cm^{- 1}. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

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