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# Curl and Divergence watch

1. Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar field or a vector field.

These are the questions and my answers...I just want to know if my answers are right...

a) curl f : is meaningless, because the curl operation can only be done o a vector field...but f is a scalar field.

b) grad f: is meaningful and a vector field

c) div F : is meaningful and a scalar field

d) curl(grad f): is meaningful and a vector field

e) grad F: meaningful and a vector field

f) grad(div F): is meaningful and a vector field

g) div(grad f): meaningful and a scalar field

h) grad(div f): meaningful and a vector field

i) curl(curl F): meaningful and a vector field

j) div(div F): meaningless, because div F is a scalar field...and div(scalar field) is meaningless

k) (grad f) x (div F): meaningless, because div F is a scalar field. (vector field) x (scalar field) = meaningless

l) div(curl(grad f)): meaningful and a scalar field

2. I studied this last year, so I could be wrong, but I think these
(Original post by Artus)

e) grad F: meaningful and a vector field

f) grad(div F): is meaningful and a vector field

h) grad(div f): meaningful and a vector field

k) (grad f) x (div F): meaningless, because div F is a scalar field. (vector field) x (scalar field) = meaningless
are wrong.
3. (Original post by Miss Mary)
I studied this last year, so I could be wrong, but I think these

are wrong.
Why are they wrong?
4. OK, let's take F = (x, y, z). Can you tell me what grad F is?
5. (Original post by DFranklin)
OK, let's take F = (x, y, z). Can you tell me what grad F is?
To be honest, I don't know...actually, I can explain my answers for all of them except for this one...because I didn't know the answer, so I looked it up in wikipedia. There it said it was a tensor, but we didn't learn that yet, so I thought it should be a vector field.
6. It's not a vector field.

Now, if f = x, what is div f?
7. (Original post by DFranklin)
It's not a vector field.

Now, if f = x, what is div f?
Its meaningless...div F = scalar field, but div f = meaningless...so I guess grad F = meaningless too. Thanks for answering, I wanted to give you a thumbs up, but it keeps saying "Please rate some other members before rating this member again."...so sorry I can't.
8. (Original post by Artus)
Why are they wrong?
grad - takes a scalar and gives back a vector
div - takes a vector and gives back a scalar
curl - takes a vector and gives back a vector

so grad of div is fine, and div of grad is fine, but grad of curl is not fine, and neither is curl of div.

Can you see that?
9. (Original post by py0alb)
grad - takes a scalar and gives back a vector
div - takes a vector and gives back a scalar
curl - takes a vector and gives back a vector

so grad of div is fine, and div of grad is fine, but grad of curl is not fine, and neither is curl of div.

Can you see that?
Yes I can see that, because grad of curl = grad of a vector field...and curl of div = curl of a scalar field...they are both meaningless...thank you

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