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  4. A sphere S1 of radius R, encloses a total charge q. If there is another concentric sphere S 2 of radius 2 R and there be no additional charges between S1 and S 2 . What is the ratio of electric flux through S 1 and S 2 ?

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Q. A sphere $S_{1}$ of radius $R$, encloses a total charge $q$. If there is another concentric sphere $S _{2}$ of radius $2 R$ and there be no additional charges between $S_1$ and $S _{2} .$ What is the ratio of electric flux through $S _{1}$ and $S _{2} ?$

Electric Charges and Fields

Solution:

$\phi=\frac{q}{\varepsilon_{0}}$
So,
$\frac{\phi_{1}}{\phi_{2}}=\frac{q_{1}}{\varepsilon_{0}} \times \frac{\varepsilon_{0}}{q_{2}}$
$=\frac{q_{1}}{q_{2}} $
$\frac{\phi_{1}}{\phi_{2}}=\frac{q}{q}=1$