- #1

- 29

- 0

## Homework Statement

I'm stuck on the following vector integral

Q(

**x**)=INT[(p(

**y**)/|

**x**-

**y**|)(d

**y**)^3

For a sphere of uniform p (so it is not a function of

**y**in this case). Where

**x**is the position vector of a point lying outside the sphere and

**y**is the position vector of a point lying inside the sphere.

## Homework Equations

## The Attempt at a Solution

I attempted this by taking advantage of the symmetry and picking

**x**to lie along the z axis. I then attempted to integrate it in spherical polar coordinates and wrote the components of

**y**in terms of theta and phi (the latter being the azimuthal angle). I wrote the volume element in spherical polars ignoring the vector notation for now. But after doing all this I get to an expression:

Q=2pi*p INT[(r^2*sin^2(theta))/(|

**x**|^2-2|

**x**|rcos(theta)+r^2)^1/2]drd(theta)

Which seem's like a very difficult integral to me.

Thanks in advance for your help.