JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Electrostatics

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 of the particle is :

Answer: (A)

Solution

Using Gauss's law for a cylindrical charge distribution, the electric field at distance

r = R

from the axis is:

E (2 π R ℓ) = \frac{ρ π R ^{2} ℓ}{ε _{0}}

E = \frac{ρR}{2 ε _{0}}

For circular motion, the electric force provides centripetal force:

q E = \frac{m v ^{2}}{R}

q \cdot \frac{ρR}{2 ε _{0}} = \frac{m v ^{2}}{R}

Kinetic energy:

K E = \frac{1}{2} m v^{2} = \frac{q E R}{2} = \frac{q ρ R ^{2}}{4 ε _{0}}

Answer: (A)

\frac{ρq R ^{2}}{4 ε _{0}}

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Single correct option