Using the Flux Formula for Different Charge Distributions

[oneplusone]

I am confused about when you can use the formula $\dfrac{q_{enc}}{\epsilon_0} = \Phi$ for flux. Is it only when you have a closed surface with point charges? What if you have a closed surface with a non-point charge?

 

[Dale]

The charge q is just the total charge enclosed by the Gaussian surface. The distribution doesn't matter. In particular, there is no distinction between point charges and a charge distribution.