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Physics Question on Electric Charge

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:

A

ρqR24∈0\frac{ρqR^2}{4∈_0}

B

ρqR22∈0\frac{ρqR^2}{2∈_0}

C

qρ4∈0R2\frac{qρ}{4∈_0R^2}

D

4∈0R2qρ\frac{4∈_0R^2}{qρ}

Answer

ρqR24∈0\frac{ρqR^2}{4∈_0}

Explanation

Solution

mv2r=2kρ×πR2qr\frac{mv^2}{r} = \frac{2kρ\times \pi R^2q}{r}

⇒ 12mv2=ρR2q4∈0\frac{1}{2}mv^2 = \frac{\rho R^2q}{4∈_0}