- #1
havarija
- 2
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I've encountered a problem in learning about the curl of a vector field.
(My learning material is the "Div, Grad, Curl and all that" from H.M. Shey.)
Introduction to problem:
The curl of a field F is defined as:
∇×F = i (∂Fz/∂y - ∂Fy/∂z) + j(∂Fx/∂z - ∂Fx/∂x) + k(∂Fy/∂x - ∂Fx/∂y)
He claims the following:
If we take:
n.(∇xF) for n = i, j, k
and they all equal 0 that we can conclude that ∇xF = 0 generally.
Is it not that we can only conclude that:
∂Fz/∂y = ∂Fy/∂z
∂Fx/∂z = ∂Fx/∂x and
∂Fy/∂x = ∂Fx/∂y
Or does this conclusion imply the following somehow?
Thanks .)
(My learning material is the "Div, Grad, Curl and all that" from H.M. Shey.)
Introduction to problem:
The curl of a field F is defined as:
∇×F = i (∂Fz/∂y - ∂Fy/∂z) + j(∂Fx/∂z - ∂Fx/∂x) + k(∂Fy/∂x - ∂Fx/∂y)
He claims the following:
If we take:
n.(∇xF) for n = i, j, k
and they all equal 0 that we can conclude that ∇xF = 0 generally.
Is it not that we can only conclude that:
∂Fz/∂y = ∂Fy/∂z
∂Fx/∂z = ∂Fx/∂x and
∂Fy/∂x = ∂Fx/∂y
Or does this conclusion imply the following somehow?
Thanks .)