Question

If there were only one type of charge in the universe, then

• A. $\oint_{s}\,\vec{E}.d\vec{s}\ne 0$ on any surface
• B. $\oint_{s}\,\vec{E}.d\vec{s}=0$ if the charge is outside the surface
• C. $\oint_{s}\,\vec{E}.d\vec{s}=\frac{q}{\varepsilon_{0}}$ if charges of magnitude $q$ were inside the surface
• D. both (b) and (c) are correct

Answer 1

Answer: (D)

According to Gauss’s theorem in electrostatics
$\oint\,\vec{E}\cdot d\,\vec{s}=\frac{q}{\varepsilon_{0}}$
Here $q$ is charge enclosed by the surface.
If the charge is outside the surface, therefore $q_{inSide} = 0$
Also, $\oint\,\vec{E}\cdot d\,\vec{s}=0$
So both (b) and (c) are correct.