(adsbygoogle = window.adsbygoogle || []).push({}); 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

[itex] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} [/itex], what is the electric field [itex] \vec{E}[/itex] in that region?

2. Relevant equations

[itex] E = -\nabla v [/itex]

3. The attempt at a solution

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

[itex] v (r, \phi, z) = r^2 sin \phi e^{\frac{-3}{z}} [/itex]

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

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

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

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

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# Homework Help: Computing for Electric Field given cylindrical coordinates of v.

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