JEE Main202224 Jun 2022Evening ShiftPhysicsElectrostaticsActual
A long cylindrical volume contains a uniformly distributed charge of density ρ . 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 :
Options
- Aρ q R 2 4 ε o
- Bρ q R 2 2 ε o
- Cq ρ 4 ε 0 R 2
- D4 ε 0 R 2 q ρ
Correct answer
A. ρ q R 2 4 ε o
Step-by-step solution
Electric field due to a long cylinder is, E = λ 2 π ε 0 r = ρ A 2 π ε 0 r If a charge q is rotating in a circle of radius r m v 2 r = q E ⇒ m v 2 r = q ρ A 2 π ε 0 r ⇒ 1 2 m v 2 = q ρ π R 2 4 π ε 0 = q ρ R 2 4 ε 0