Electric Potential V(x,y,z): Sketch Electric Field Lines

[Fabio010]

V(x,y,z) = (Vo).e^[(-k|z|)].cos(kx)

Find the electric field everywhere. Sketch the electric field lines in the x − z plane. Attempt:

∂V/∂x = -Ex

-Ex = -k(Vo).e^[(-k|z|)].sin(kx) Ex = k(Vo).e^[(-k|z|)].sin(kx)

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-Ez = -(Vo).k.e^[(-k|z|)].cos(kx) if z >=0

Ez = (Vo).k.e^[(-k|z|)].[cos(kx)] if z >=0

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-Ez = +(Vo).e^[(-k|z|)].cos(kx) if z<0

Ez =(Vo).e^[(-k|z|)].[-cos(kx)]My problem is sketching the electric field lines. Any tips?

 

[frogjg2003]

Your derivatives are wrong.
You're missing a factor of k in the x term. You don't use the product rule in z.

 

[Fabio010]

I was confounding z with k that's why i used the product rule :)

But even with that equations i don't now how to sketch the lines :/

 

[frogjg2003]

As for plotting, try starting at any "obvious" points and paths. For example z=0, x=±nπ/2.

 

[frogjg2003]

Also consider how the field behaves as z→±∞