Rankers Physics

Gauss's Law: Practice Problem & Solution

In the arrangement of charges shown, the dotted boundary represents a Gaussian surface . For this surface , Gauss's law has the form \[ \oint_{}^{}\overrightarrow{E}.\overrightarrow{ds}=\frac{q}{\varepsilon_{0}} .\] Select the correct alternative \[ \overrightarrow{E_{1}},\overrightarrow{E_{2}}, \overrightarrow{E_{3}} and \overrightarrow{E_{4}} \] are electric field vectors due to these four charges respectively. Gauss's Law diagram: In the arrangement of charges shown, the dotted
\[ q=q_{2}+q_{4}\]
\[ q=q_{2}+q_{4}-q_{1}-q_{3}\]
\[ \overrightarrow{E}=\overrightarrow{E_{1}}+\overrightarrow{E_{2}}+\overrightarrow{E_{3}}+\overrightarrow{E_{4}}\]
\[ \overrightarrow{E}=\overrightarrow{E_{2}}+\overrightarrow{E_{4}}\]

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Gauss's Law. Understanding the underlying formula is key to arriving at the correct answer below:

In Gauss law q represents total charge enclosed within the gaussian surface. so,

\[ q= q_{2} + q_{4}\]

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