The distribution of some charges on two Gaussian surfaces $A$ and $B$ are as shown in the figure. If…

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 $\frac{\phi_A}{\phi_B}=$

1. $-\frac{1}{5}$
2. $-3$
3. $-\frac{3}{2}$
4. $-\frac{3}{4}$

Solution

The distribution of charges on two Gaussian surfaces $A$ and $B$ are shown below
Flux through a closed surface, $\phi=\frac{q_{\text {net }}}{\varepsilon_0}$ $q_{\text {net }}=$ net charge enclosed by the surface Here, $\left(q_{\text {net }}\right)_A=$ charge enclosed by surface $ A=q+3 q-2 q-5 q=-3 q $ And $\left(q_{\text {net }}\right)_B=-q+3 q+2 q=4 q$ So, $\frac{\phi_A}{\phi_B}=\frac{-3 q / \varepsilon_0}{4 q / \varepsilon_0}=\frac{-3}{4}$

Asked in: AP EAMCET 2022 (07 Jul Shift 2)

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