Question

A particle of mass $5\times {10}^{-6}\text{g}$ is kept over a large horizontal sheet of charge density $4\times {10}^{-6}{\text{C/m}}^2$. What charge should be given to this particle so that if released, it remains in equilibrium? [Take ${ϵ}_0=9\times {10}^{-12}{\text{C}}^2{\text{/Nm}}^2$]

• A. $2.3\times {10}^{-13}\text{C}$
• B. $3.3\times {10}^{-13}\text{C}$
• C. $4.6\times {10}^{-13}\text{C}$
• D. $9.2\times {10}^{-13}\text{C}$

Answer 1

The correct option is A $2.3\times {10}^{-13}\text{C}$

Given,
Surface charge density of the given sheet, $\sigma =4\times {10}^{-6}{\text{C/m}}^2$

The electric field above the sheet is $E=\frac{\sigma }{2{ϵ}_0}$
Substituting the values,
$E=\frac{4\times {10}^{-6}}{2\times 9\times {10}^{-12}}$

$\Rightarrow E=2.2\times {10}^5\text{N/C}$


For the particle to not fall down, the electrostatic force on it should balance its weight. So, from the above FBD,
$qE=mg$
where,
mass of the particle, $m=5\times {10}^{-6}\text{g}$
charge of the particle $=q$
$\Rightarrow q=\frac{mg}{E}$

$\Rightarrow q=\frac{5\times {10}^{-9}\times 10}{2.2\times {10}^5}$

$\therefore q=2.3\times {10}^{-13}\text{C}$

Hence, option (a) is correct answer.