Question

If there is only one type of charge in the universe, then what is the flux to the entire universe.
($\overrightarrow{E}\to$ Electric field, $\overrightarrow{ds}\to$ Area vector)

• A. $\oint \overrightarrow{E}\cdot \overrightarrow{ds}\ne 0$ on any surface
• B. $\oint \overrightarrow{E}\cdot \overrightarrow{ds}$ could not be defined
• C. $\oint \overrightarrow{E}\cdot \overrightarrow{ds}=\infty$ if charge is inside
• D. $\oint \overrightarrow{E}\cdot \overrightarrow{ds}=0$ if charge is outside, $=\frac{q}{{ϵ}_0}$ if charge is inside

Answer 1

The correct option is D $\oint \overrightarrow{E}\cdot \overrightarrow{ds}=0$ if charge is outside, $=\frac{q}{{ϵ}_0}$ if charge is inside

According to Gauss’s law - the total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

Hence if the charge is outside, the total electric flux is zero and if the charge is inside, the total electric flux will be $\frac{q}{{ϵ}_0}$.

Hence option D is correct.