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vote
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dotting gradient in spherical coordinates with displacement vector
The gradient in spherical coordinates is given by:
$\nabla f = \left(\frac{\partial f}{\partial r}, \frac{1}{r} \frac{\partial f}{\partial \theta}, \frac{1}{r \sin \theta} \frac{\partial f}{\partial ...
3
votes
3answers
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Surface Element in Spherical Coordinates
In spherical polars,
$$x=r\cos(\phi)\sin(\theta)$$
$$y=r\sin(\phi)\sin(\theta)$$
$$z=r\cos(\theta)$$
I want to work out an integral over the surface of a sphere - ie $r$ constant. I'm able to derive ...
4
votes
2answers
170 views
How do I convert a vector field in Cartesian coordinates to spherical coordinates?
I have a vector field in terms of $\mathbf{\hat i}$, $\mathbf{\hat j}$, and $\mathbf{\hat k}$,
$$\mathbf{F} = x\mathbf{\hat i} + y\mathbf{\hat j} + z\mathbf{\hat k}$$
How do I convert it to the ...
