# Computing for Electric Field given cylindrical coordinates of v.

1. Feb 7, 2012

### jhosamelly

1. The problem statement, all variables and given/known data

If the scalar electric potential v in some region is given in cylindrical coordinates by
$v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}}$, what is the electric field $\vec{E}$ in that region?

2. Relevant equations

$E = -\nabla v$

3. The attempt at a solution

So, first I need to change the cylindrical coordinates to cartesian coordinates.

$v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}}$

$v (r, \phi, z) = (x^2 + y^2) \frac{y}{r} e^{\frac{-3}{z}}$

$v (r, \phi, z) = (x^2 + y^2) \frac{y}{\sqrt{x^2 + y^2}} e^{\frac{-3}{z}}$

$v (r, \phi, z) = y e^{\frac{-3}{z}} \sqrt{x^2 + y^2}$

** so is this already the cartesian coordinates? can I perform the gradient now?

2. Feb 7, 2012

### vela

Staff Emeritus
3. Feb 7, 2012

### jhosamelly

ow, I see. We were not given that formula though. So I think I need to do it in cartesian coordinates. Thanks.