# Thread: Vector field -> rotational

1. ## Vector field -> rotational

Show that any vector field of the form:
$\displaystyle F(x,y,z) = f(x) i + g(y) j + h(z) k$ where f, g and h are differentiable, is not rotational

2. Find the curl of F.

Curl F = $\displaystyle \Big( \frac { \partial}{\partial y} h(z) - \frac {\partial}{\partial z} g(y) \Big) \hat{i} - \Big( \frac { \partial}{\partial x} h(z) - \frac {\partial}{\partial z} f(x) \Big) \hat{j} + \Big( \frac { \partial}{\partial x} g(y) - \frac {\partial}{\partial y} f(x) \Big) \hat{k}$

And you can clearly see that Curl F = 0.

3. Originally Posted by Random Variable
Find the curl of F.

Curl F = $\displaystyle \Big( \frac { \partial}{\partial y} h(z) - \frac {\partial}{\partial z} g(y) \Big) \hat{i} - \Big( \frac { \partial}{\partial x} h(z) - \frac {\partial}{\partial z} f(x) \Big) \hat{j} + \Big( \frac { \partial}{\partial x} g(y) - \frac {\partial}{\partial y} f(x) \Big) \hat{k}$

And you can clearly see that Curl F = 0.
Ok. Thank you