Question

Two particle of equal mass $m$ and charge $q$ are placed at a distance of $16cm$. They do not experience any force. The value of $\frac{q}{m}$ is :

• A. $\sqrt{\frac{\pi {\epsilon }_0}{G}}$
• B. $L$
• C. $\sqrt{\frac{G}{\pi {\epsilon }_0}}$
• D. $\sqrt{4\pi {\epsilon }_{0}G}$

Answer 1

Answer: (D)

$\text{Step 1: Electrostatic force between particles}$

Applying Coulomb's law,
$F_e=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{(0.16m{)}^2}$ $....\left(1\right)$

$\text{Step 2: Gravitational force between particles}$

Applying Newton's law of universal gravitation,

$F_G=G\frac{m_1{m}_2}{r^2}=G\frac{m^2}{(0.16{)}^2}$ $....\left(2\right)$

$\text{Step 3: Net force experienced}$

Since net force experienced by the particle is zero, therefore electrostatic force and gravitational force would be equal.

$\therefore F_e=F_G$

From $\left(1\right)$ and $\left(2\right)$

$\frac{1}{4\pi {ϵ}_0}\frac{q^2}{(0.16{)}^2}=G\frac{m^2}{(0.16{)}^2}$

$\Rightarrow \frac{q}{m}=\sqrt{4\pi {ϵ}_{0}G}$

Hence Option D is correct