# 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.

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## Answers and Replies

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
Science Advisor
Gold Member
First of all you have to specify the cube, i.e., its location and orientation. If the origin is contained inside the cube, it's not a good idea to use Gauss's Law and the volume integral over the divergence, because you have to find out how to treat the non-trivial singularity at the origin.

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!