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Two identical charges repel each other with a force equal to $10 \mathrm{mg}$ wt when they are $0.6 \mathrm{~m}$ a part in air $\left(g=10 \mathrm{~ms}^{-2}\right)$. The value of each charge is
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Verified Answer
The correct answer is:
$2 \mu \mathrm{C}$
Coulomb force is given by
$$
\begin{aligned}
F &=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} \\
\therefore\left(10 \times 10^{-3}\right) \times 10 &=\frac{\left(9 \times 10^{9}\right) \times q^{2}}{(0.6)^{2}} \\
\text { or } \quad q^{2} &=\frac{10^{-1} \times 0.36}{9 \times 10^{9}} \quad\left[\because q_{1}=q_{2}=q\right] \\
&=4 \times 10^{-12} \\
\therefore \quad q &=2 \times 10^{-6} \mathrm{C}=2 \mu \mathrm{C}
\end{aligned}
$$
$$
\begin{aligned}
F &=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} \\
\therefore\left(10 \times 10^{-3}\right) \times 10 &=\frac{\left(9 \times 10^{9}\right) \times q^{2}}{(0.6)^{2}} \\
\text { or } \quad q^{2} &=\frac{10^{-1} \times 0.36}{9 \times 10^{9}} \quad\left[\because q_{1}=q_{2}=q\right] \\
&=4 \times 10^{-12} \\
\therefore \quad q &=2 \times 10^{-6} \mathrm{C}=2 \mu \mathrm{C}
\end{aligned}
$$
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