Find Flux Through Cube & Sphere

[dpa]

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.

 

[BruceW]

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

 

[CAF123]

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]

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!