# Math Help - Divergence Help

1. ## Divergence Help

Hello,

I need some help with divergence

${\bf{E}} = \frac{1}{\varepsilon }\left( {\frac{{\partial \phi }}{{\partial {z^{}}}}{\bf{i}} - \frac{{\partial \phi }}{{\partial x}}{\bf{k}}} \right)$

and

$\nabla = {\bf{i}}\frac{\partial }{{\partial x}} + {\bf{j}}\frac{\partial }{{\partial y}} + {\bf{k}}\frac{\partial }{{\partial z}}$

Show that

$\nabla \cdot {\bf{E}} = 0$

When I work with numbers, all is good but now I'm confused. Is the answer related to the fact that the i component only contains z and the k only contains x? So that these will become 0?

Thanks for any help.

2. ## Re: Divergence Help

Hey mark090480.

You should use the fact that <i,j> = <i,k> = <j,k> = 0 and expand out the representation of E in terms of its components <a,b,c> = ai + bj + ck. where a,b,c are real valued variables.