Question 230: Electrostatics & Capacitance

Question

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 	imes 10^{-8} \mathrm{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 	imes 10^{-3} \mathrm{~N}$. The distance between them is (Take $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}$ as $9 	imes 10^9$ in SI units)

Accepted Answer

$$\begin{aligned}
& \mathrm{F}=\frac{\mathrm{k}\left(\frac{	heta}{2}ight)\left(\frac{	heta}{2}ight)}{\mathrm{r}^2} \
& 9 	imes 10^{-3}=\frac{9 	imes 10^9 	imes\left(4 	imes 10^{-8}ight) 	imes 4 	imes 10^{-8}}{4 	imes \mathrm{r}^2} \
& \mathrm{r}^2=\frac{9 	imes 10^9 	imes 16 	imes 10^{-16}}{4 	imes 9 	imes 10^{-3}}=4 	imes 10^{-4} \
& \mathrm{r}=2 	imes 10^{-2} \mathrm{~m} \Rightarrow 2 \mathrm{~cm}
\end{aligned}$$

Answer

1 cm

Answer

2 cm

Answer

4 cm

Answer

3 cm

Electrostatics & Capacitance

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