- #1

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**Curl div....**

## Homework Statement

f is a scalar field. What does div(f) curl(f) rotgrad(f) divgrad(f) stand for?

I need to know if a scalar field can have the meanings of roration and diverge like a vector field

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- Thread starter Engels
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- #1

- 12

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f is a scalar field. What does div(f) curl(f) rotgrad(f) divgrad(f) stand for?

I need to know if a scalar field can have the meanings of roration and diverge like a vector field

- #2

lanedance

Homework Helper

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if f is a scalar field, then grad(f) is a vector fields## Homework Statement

f is a scalar field. What does div(f) curl(f) rotgrad(f) divgrad(f) stand for?

I need to know if a scalar field can have the meanings of roration and diverge like a vector field

div(f) makes no sense as f is a scalar, and div operates on vectors , curl(f) doesn't make sense for the same reasons

i'm guess rotgrad(f) = curl(grad(f)) which is ok, though i remember correctly its zero

and divgrad(f) = div(grad(f)) which is ok as well

have a look at this

http://en.wikipedia.org/wiki/Vector_calculus_identities

Last edited:

- #3

- 2,967

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div and curl are only defined for vector fields. grad is only defined for scalar fields.

The result of div is a scalar and the result of grad and curl is a vector. Therefore, these are the second spatial derivatives that you can construct:

[tex]

\mathrm{div} (\mathbf{grad} \, \phi) = \nabla^{2} \, \phi

[/tex]

[tex]

\mathrm{div} (\mathbf{curl} \, \mathbf{A}) = 0

[/tex]

[tex]

\mathbf{grad} (\mathrm{div} \, \mathbf{A})

[/tex]

[tex]

\mathbf{curl}(\mathbf{grad} \, \phi) = \mathbf{0}

[/tex]

[tex]

\mathbf{curl} (\mathbf{curl} \, \mathbf{A}) = \mathbf{grad} (\mathrm{div} \, \mathbf{A}) - \nabla^{2} \, \mathbf{A}

[/tex]

where [itex]\nabla^{2}[/itex] stands for the Laplace differential operator (Laplacian).

- #4

lanedance

Homework Helper

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fixed up above - missed the curl(f) bit

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