Question

$q_{1},q_{2},q_{3}$ and $q_{4}$ are point charges located at point as shown in the figure and $S$ is a spherical Gaussian surface of radius $R.$ Which of the following is true according to the Gauss's law:-

• A. $(\oint)_{s}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{q_{1}+q_{2}+q_{3}}{2_{\epsilon_{0}}}$
• B. $(\oint)_{s}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{q_{1}+q_{2}+q_{3}}{{\epsilon_{0}}}$
• C. $(\oint)_{s}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{q_{1}+q_{2}+q_{3} + q_4}{{\epsilon_{0}}}$
• D. None of the above

Answer 1

Answer: (D)

By using $\int \overset{ \rightarrow }{E}\cdot \overset{ \rightarrow }{d A}=\frac{1}{ϵ_{0}}\left(Q_{enc}\right)$
Here $\overset{ \rightarrow }{E} \rightarrow $ net electric field.