- #1

havarija

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(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 .)