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If same charge $q$ is placed inside a sphere and cube having radius 1 m and side 2 m respectively. What will be the ratio of flux passing through them?
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Verified Answer
The correct answer is:
$1: 1$
According to Gauss's law, electric flux passing through a closed surface is equal to $\frac{1}{\varepsilon_0}$ times the charge (q) enclosed by the surface
i.e.
$\phi=\frac{\mathrm{q}}{\varepsilon_0}$
Since, cube and sphere, both enclose same charge, therefore flux passing through cube and sphere is same. i.e. $\phi_{\text {sphere }}=\phi_{\text {cube }}$
$\therefore \quad \phi_{\text {sphere }}: \phi_{\text {cube }}=1: 1$
i.e.
$\phi=\frac{\mathrm{q}}{\varepsilon_0}$
Since, cube and sphere, both enclose same charge, therefore flux passing through cube and sphere is same. i.e. $\phi_{\text {sphere }}=\phi_{\text {cube }}$
$\therefore \quad \phi_{\text {sphere }}: \phi_{\text {cube }}=1: 1$
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