Question

The flux associated with a spherical surface is $104{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$. What will be the flux, if the radius of the spherical shell is doubled?

Answer 1

Gauss Law:

1. The electric flux is the total number of electric field lines passing a given area in a unit of time.
2. Gauss Law states that the total electric flux($\mathrm{\varphi }$) out of a closed surface is equal to the charge($\mathrm{q}$) enclosed divided by the permittivity(${\mathrm{\epsilon }}_0$), that is $\mathrm{\varphi }=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$.
3. The total electric flux($\mathrm{\varphi }$) is proportional to the charge($\mathrm{q}$) enclosed.
4. Here, the electric flux associated with the sphere is $104{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$.
5. The radius of the spherical shell is doubled then the flux associated with the spherical surface remains unchanged since the charge enclosed in the system always remains unchanged.

Therefore, if the radius of the spherical shell is doubled the electric flux associated with the spherical surface remains unchanged.