Verified Solution • 2025–26 Session moderate

QJEEM22Phc7db: JEE Main 2022 Physics - Class 12 JEEM22Phc7db Solution: A long cylindrical volume contains a uniformly distributed…

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 :

Multiple Choice Options

  • A ρqR24ε0{{\rho q{R^2}} \over {4{\varepsilon _0}}}
  • B ρqR22ε0{{\rho q{R^2}} \over {2{\varepsilon _0}}}
  • C qρ4ε0R2{{q\rho } \over {4{\varepsilon _0}{R^2}}}
  • D 4ε0R2qρ{{4{\varepsilon _0}{R^2}} \over {q\rho }}

Step-by-Step Verified Solution

mv2r=2kρ×πR2qr{{m{v^2}} \over r} = {{2k\rho \times \pi {R^2}q} \over r}

⇒12mv2=ρR2q4ε0\Rightarrow {1 \over 2}m{v^2} = {{\rho {R^2}q} \over {4{\varepsilon _0}}}

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