# Homework Help: Flux through cube

1. Sep 18, 2013

### dpa

Flux through sphere

1. The problem statement, all variables and given/known data
Given $\vec{F}=\frac{\vec{r}}{r^2}$ and unit sphere, find the flux through the surface of the cube.

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

3. The attempt at a solution
After the above formula, I do not have idea how to use divergence in spherical coordinate system.

Last edited: Sep 18, 2013
2. Sep 18, 2013

### BruceW

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

3. Sep 18, 2013

### CAF123

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.

4. Sep 18, 2013

### vanhees71

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!