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A point charge causes an electric flux of $-1.0 \times 10^3$ $\mathrm{Nm}^2 / \mathrm{C}$ to pass through a spherical Gaussian surface of $10.0 \mathrm{~cm}$ radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
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Given, Flux $=\phi=-1.0 \times 10^3 \mathrm{Nm}^2 \mathrm{C}^{-1}$ $\varepsilon_0=8.854 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ (taken), $\mathrm{q}=$ ?
(a) By Gauss's law, electric flux $\phi=q / \varepsilon_0$ It is independent of dimensions and shape of the Gaussian surface.
So, $\phi=-1.0 \times 10^3 \mathrm{Nm}^2 \mathrm{C}^{-1}$
(b) We have,
$$
\begin{aligned}
q &=\phi \varepsilon_0=-10^3 \times 8.854 \times 10^{-12} \\
&=-8.854 \times 10^{-9} \mathrm{C} .
\end{aligned}
$$
(a) By Gauss's law, electric flux $\phi=q / \varepsilon_0$ It is independent of dimensions and shape of the Gaussian surface.
So, $\phi=-1.0 \times 10^3 \mathrm{Nm}^2 \mathrm{C}^{-1}$
(b) We have,
$$
\begin{aligned}
q &=\phi \varepsilon_0=-10^3 \times 8.854 \times 10^{-12} \\
&=-8.854 \times 10^{-9} \mathrm{C} .
\end{aligned}
$$
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