= electric flux
where
This solution to problem 6 will NOT be given on your formula sheet
describes charge density as a function of distance to the origin. Since the Gaussian sphere is fixed at radius
we use a tilde to denote the variable of integration used to calculate the charge enclosed by the Gaussian sphere.
If the field point
, the radius of the nonuniformly (but symmetrically charged sphere), then Gauss' law is:
But also,
(using the surface area of a sphere)