Question

Which of the following holds if there was only one type of charge in the universe?

• A. $\oint_{s} \, \, \overset{ \rightarrow }{E}\cdot d\overset{ \rightarrow }{s}\neq 0$ on any surface.
• B. $\oint_{s} \, \, \overset{ \rightarrow }{E}\cdot d\overset{ \rightarrow }{s}=0$ if the charge is outside the surface.
• C. $\oint_{s} \, \overset{ \rightarrow }{E}\cdot d\overset{ \rightarrow }{s}=\frac{q}{\epsilon _{0}}$ if charge of magnitude $q$ were inside the surface.
• D. Both $\left(\right.B\left.\right)$ and $\left(\right.C\left.\right)$ are correct.

Answer 1

Answer: (D)

According to Gauss’s theorem in electrostatics $\oint_{e} \, \overset{ \rightarrow }{E} \cdot \overset{ \rightarrow }{d} s = \frac{q}{\epsilon _{0}}$
Here $q$ is charge enclosed by the surface.If the charge is outside the surface, therefore $q_{s n s i d e}=0$ Also,
$\oint_{e} \, \overset{ \rightarrow }{E} \cdot \overset{ \rightarrow }{d} s = 0$ .So both (b) and (c) are correct.