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 $g =10\, m / s ^{2}$ )

• 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 m g=q E $
$\Rightarrow m g=q \frac{\sigma}{\varepsilon_{0}}$
(As $E=\frac{\sigma}{\varepsilon_{0}}$, near a conducting surface)
Hence, $ \sigma=\frac{\varepsilon_{0} m g}{q}$
Here, $m=2 \times 10^{-6} kg , $
$q=5 \times 10^{-6} C$ $g=10 m / s ^{2}$ and
$\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} / Nm ^{2}$
Hence,
$\sigma=\frac{8.85 \times 10^{-12} \times 2 \times 10^{-6} \times 10}{5 \times 10^{-6}}$
$=35.4 \times 10^{-12} C / m$