Q. $q_{1},q_{2},q_{3}$ 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) $\oint_{s}^{\ }{\left( {\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3} \right).d\overrightarrow{A} = \frac{q_{1} + q_{2} + q_{3}}{2\varepsilon_{0}}}$
B) $\oint_{s}^{\ }{\left( {\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3} \right).d\overrightarrow{A} = \frac{{(q}_{1} + q_{2} + q_{3})}{\varepsilon_{0}}}$
C) $\oint_{s}^{\ }{\left( {\overrightarrow{E}}_{1} + {\overrightarrow{E}}_{2} + {\overrightarrow{E}}_{3} \right).d\overrightarrow{A} = \frac{{(q}_{1} + q_{2} + q_{3} + q_{4})}{\varepsilon_{0}}}$
D) None of the above
Explanation
(b) By using $\int_{}^{}{\overrightarrow{E}.\overrightarrow{dA} = \frac{1}{\varepsilon_{0}}\lbrack Q_{enc}\rbrack}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.