Flux through cube

Flux through sphere

Homework Statement

Given $\vec{F}=\frac{\vec{r}}{r^2}$ and unit sphere, find the flux through the surface of the cube.

Homework Equations

Surface Integral of F dS=volume integral of Div. F d^3r

The Attempt at a Solution

After the above formula, I do not have idea how to use divergence in spherical coordinate system.

Last edited:

BruceW
Homework Helper
why not do it the easier way by using F dS ?

CAF123
Gold Member
I do not have idea how to use divergence in spherical coordinate system.

You do not need to worry so much about the divergence in SPs. Just compute the divergence of ##\vec{F}## using the identity for ##\nabla \cdot (\phi \vec{a})##, where ##\phi## and ##\vec{a}## are scalar and vector fields respectively.

vanhees71
Last but not least, it's a pretty unusual long-ranged field. Are you sure that there isn't $r^3$ in the denominator? Better check your problem again!