Question

The diagram shows four charges $q_1,q_2,q_3$, and $q_4$ all lying in the plane of the page. The diagram also shows the dotted circle that represents the cross-section of a spherical Gaussian surface. Point $P$ is a single point on that surface.
Which of the charges contributes to the electric field at point $P$?

• A. $q_1$ and $q_3$
• B. $q_2$ and $q_4$
• C. $q_1$ and $q_2$
• D. $q_3$ and $q_4$
• E. $q_1,q_2,q_3$, and $q_4$

Answer 1

Answer: (B)

$q_2$ and $q_4$

Gauss's theorem states if a closed surface encloses a charge , then surface integral of the electric field over the closed surface is $1/{\epsilon }_0$ times of the total charge enclosed by the surface ,

$\oint \overrightarrow{E}.\overrightarrow{dS}=Q/{\epsilon }_0$

It is clear that $q_2$ and $q_4$ are the charges enclosed by gaussian surface therefore only these two will contribute to the electric field at point P.