Question

A particle of mass $2\times 10^{-6}kg$ with a charge $5\times 10^{-6}C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume ${\in }_0=8.85\times 10^{-12}{C}^2{N}^{-1}{M}^{-2}$ and $g=10m/s^2$ )

• A. $35.4\times 10^{-12}\frac{C}{m^2}$
• B. $23.6\times 10^{-12}\frac{C}{m^2}$
• C. $53.1\times 10^{-12}\frac{C}{m^2}$
• D. $17.7\times 10^{-12}\frac{C}{m^2}$

Answer 1

Answer: (A)

As particle hangs over the surface as shown above weight of particle $=$ repulsive electrostatic force
$\Rightarrow mg=qE$
$\Rightarrow mg=q\frac{\sigma }{{\epsilon }_0}$
(As $E=\frac{\sigma }{{\epsilon }_0}$, near a conducting surface)
Hence, $\sigma =\frac{{\epsilon }_{0}mg}{q}$
Here, $m=2\times 10^{-6}kg,$
$q=5\times 10^{-6}C$ $g=10m/s^2$ and
${\epsilon }_0=8.85\times 10^{-12}{C}^2/N{m}^2$
Hence,
$\sigma =\frac{8.85\times 10^{-12}\times 2\times 10^{-6}\times 10}{5\times 10^{-6}}$
$=35.4\times 10^{-12}C/m$