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. $(\oint {)}_s\left({\vec{E}}_1+{\vec{E}}_2+{\vec{E}}_3\right)\cdot d\vec{A}=\frac{q_1+q_2+q_3}{2_{{ϵ}_0}}$
• B. $(\oint {)}_s\left({\vec{E}}_1+{\vec{E}}_2+{\vec{E}}_3\right)\cdot d\vec{A}=\frac{q_1+q_2+q_3}{{ϵ}_0}$
• C. $(\oint {)}_s\left({\vec{E}}_1+{\vec{E}}_2+{\vec{E}}_3\right)\cdot d\vec{A}=\frac{q_1+q_2+q_3+q_4}{{ϵ}_0}$
• D. None of the above

Answer 1

Answer: (D)

By using $\int \overrightarrow{E}\cdot \overrightarrow{\mathrm{dA}}=\frac{1}{{ϵ}_0}\left(Q_{enc}\right)$
Here $\overrightarrow{E}\to$ net electric field.