The distribution of some charges on two Gauss | vedclass

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(D) According to Gauss's Law,the electric flux $\phi$ through a closed surface is given by $\phi = \frac{q_{	ext{net}}}{\varepsilon_0}$,where $q_{	e

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$-\frac{3}{4}$

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(D) According to Gauss's Law,the electric flux $\phi$ through a closed surface is given by $\phi = \frac{q_{	ext{net}}}{\varepsilon_0}$,where $q_{	ext{net}}$ is the net charge enclosed by the surface.For surface $A$,the charges enclosed are $q$,$3q$,$-2q$,and $-5q$. Therefore,$(q_{	ext{net}})_A = q + 3q - 2q - 5q = -3q$.Thus,$\phi_A = \frac{-3q}{\varepsilon_0}$.For surface $B$,the charges enclosed are $3q$,$-q$,and $2q$. Therefore,$(q_{	ext{net}})_B = 3q - q + 2q = 4q$.Thus,$\phi_B = \frac{4q}{\varepsilon_0}$.Now,the ratio of the fluxes is:$\frac{\phi_A}{\phi_B} = \frac{-3q / \varepsilon_0}{4q / \varepsilon_0} = -\frac{3}{4}$.

The distribution of some charges on two Gaussian surfaces $A$ and $B$ are as shown in the figure. If $\phi_A$ and $\phi_B$ are electric fluxes linked with the surfaces $A$ and $B$ respectively,then $\frac{\phi_A}{\phi_B}=$

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