- #1

- 57

- 4

## Homework Statement

$$\bar{v}=\nabla \times \psi \hat{k}$$

The problem is much bigger, i know how a rotor or curl is calculated in cylindrical coordinates, but i'm just asking to see what would be the "determinant" rule for this specific curl.

## Homework Equations

$$\psi$$ is in cylindrical coordinates (r,theta,z) and depends only on r and z, not theta meaning $$\psi(r,z)$$

## The Attempt at a Solution

I'm asked to write the velocity field in therms of the current function psi, and i know i have to do it with said equation above, i believe the determinant rule used (given this is a demonstration and i already know the answer) was

(i tried doing a matrix and i couldn't, but the bottom line of the determinant looks like it was 0 & psi & 0, so the result should yield) $$\bar{v}=(\frac{-1}{r} \frac{\partial \psi}{\partial z}, 0, \frac{1}{r}\frac{\partial \psi}{\partial r})$$