Question

$q_{1},\mspace{6mu} q_{2},\mspace{6mu} q_{3}$ and$q_{4}$ are point charges located at points 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. $\oint_{s}^{}{({\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3}).d\overrightarrow{A}} = \frac{q_{1} + q_{2} + q_{3}}{2\varepsilon_{0}}$
• B. $\oint_{s}^{}{({\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3}).d\overrightarrow{A}} = \frac{(q_{1} + q_{2} + q_{3})}{\varepsilon_{0}}$
• C. $\oint_{s}^{}{({\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3}).d\overrightarrow{A}} = \frac{(q_{1} + q_{2} + q_{3} + q_{4})}{\varepsilon_{0}}$
• D. None of the above

Answer 1

Answer: (B)

$\oint_{s}^{}{({\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3}).d\overrightarrow{A}} = \frac{(q_{1} + q_{2} + q_{3})}{\varepsilon_{0}}$

Answer 2

By using $\int_{}^{}{\overset{\rightarrow}{E} \cdot \overset{\rightarrow}{dA}} = \frac{1}{\varepsilon_{0}}(Q_{enc})$