Curl, Divergence, and Gradient?
Let f be a scalar field and F be a vector field. Sate whether each expression is meaningful. If not, explain why. If so, state whether it is a scalar or vector field.
a) curl f
b) grad f
c) div F
d) curl (grad F)
e)grad F
f) grad (div F)
g)div(grad f)
h) grad(div f)
i)curl(curl F)
j) div(div F)
k) (grad f)X(div F)
l) div(curl(grad f))
Answers & Comments
Verified answer
Most of these are pretty trivial.
Curl acts on a vector field and produces a vector field
Div acts on a vector field and produces a scalar field
Grad acts on a scalar field and produces a vector field
I'll just answer a few of them to show you how
a) meaningless, f is a scalar
b) grad operates on a scalar field so this is OK
d) curl (grad F) Can't take grad of a vector field so this is meaningless
i) curl (curl F) this is OK, F is a vector and curl F produces a new vector field. So you can take the curl again.
they're the first mathematical kit you utilize to verify how electric powered and magnetic fields relate to a minimal of one yet another and to count of countless varieties. I spent an entire twelve months doing this as portion of my undergraduate application in physics and electric powered engineering.