# Exam Tomorrow - Divergance of a Vector Field

1. Jan 11, 2006

### Lee_Speakman

Hi all, first I think i should introduce myself, my name is Lee and a 2nd year student studying Electronic Engineering at Liverpool University England. This will be my last ever Maths exam so Id like to pass it first time! (Math isnt my strong point) and I simple wish to pass the Math module

I have two questions that always comes up 1, these are past exam paper questions, I can do the first part for the first question but not the second and Laplace Questions after it.

and:

If anyone can help with these questions with a step by step example It would be a big boost and I will buy you a virtual beer!

In the mean time I will plug away trying to understand them,

kind regards Lee

2. Jan 11, 2006

### Tom Mattson

Staff Emeritus
We typically require that students show some work before receiving help, but I will point you in the right direction. If you get stuck after trying what I advise, post what you have done and we will get you un-stuck.

For the first part, write down the vector $\vec{v}$ in Cartesian components: $\vec{v}=v_x\hat{i}+v_y\hat{j}+v_z\hat{k}$, and then divide each component by $\phi$, then apply the divergence operator to that vector field. Note that you really only have to do the work for one term, thanks to symmetry.

I would take a Cartesian approach to the other parts as well. In fact the problem itself gives you that exact same hint. Just remember that $|\vec{r}|=\sqrt{x^2+y^2+z^2}$.

Last edited: Jan 11, 2006
3. Jan 11, 2006

### Benny

For the Laplace question, you've got the expression for grad(1/r) = *. All you then need to do is calculate div(*).

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