Question about cross and dot product

[leonne]

Homework Statement

Note: $$\nu$$ is del could not find it...

I need to prove the $$\nu$$*E=0
and $$\nu$$ x E=-dB/dt

Homework Equations

E(s$$\phi$$zt)=(Acos(Kz=wt)/s)s^

The Attempt at a Solution

so for the first one $$\nu$$*E=0 I thought it would be
d/ds(E) but what they did was 1/s d/ds(s E) no idea why they did it. Is it because its S^? I thought i remember doing something like this.
for the cross product
d/ds d/d$$\phi$$ d/dz
E 0 0

...I got the right answer but they got 0+dE/dZ $$\phi$$^-1/s dE/d$$\phi$$ z^
no idea how they got the z^ i thought it was 0, well it does =0 but where did the -1/s come from?
thanks for the help[STRIKE][STRIKE][/STRIKE][/STRIKE]

 

[lanedance]

try writing all youyr code in a single tex banner & to write del (\nabla), so you want to show:
$$\nabla \bullet E = 0$$

how about directly applying the product? I can;t really understand the form of your electric field - mayeb you can re-write it?

 

[leonne]

hmm can't edit my post
so need to show that
$$\nabla$$ $$\bullet$$ E=0
$$\nabla$$ $$\times$$ E= -dB/dT
Well its a wave function
And i need to show that E satisfy Maxwell equation and the boundary conditions.
boundary condition E parallel =0 and B perpendicular=0
lets say E was x^ for the dot product
(d/dx+d/dy+d/dz)(E x^+0+0) so i would have dE/dx am i wrong?