Ok, so I know the curl represents how much something rotates about an axis.(adsbygoogle = window.adsbygoogle || []).push({});

Let's assume we have a vector field F = Fx + Fy + Fz, where x y and z are direction vectors.

So the rotation about the Z axis is made possible by a change in the Y direction and a change in the X direction.

But the formula for the curl around the Z-axis is given by: dFy/dx - dFx/dy

I pulled that from Equation 3 here: http://www.maxwells-equations.com/curl/curl.php

How does this represent the rotation about the X axis? I'm reading dFy/dx - dFx/dy as:

The change in the Y vector along the X direction, and The change in the X vector along the Y direction.

How does this represent curl around the Z axis? Also, why is it dFy/dx - dFx/dy?

Shouldn't dFy/dx still be a vector pointing in the Y direction, and dFx/dy a vector pointing in the X direction? So you can't just subtract them because they are perpendicular to each other, right? It's like saying I have Velocity in the Y direction and Velocity in the X direction, so the net velocity is the Y direction minus the X direction, which is incorrect. You have to use Pythagorean's Theorem to find the net velocity, so shouldn't you do the same here? As in the net curl is going to be sqrt[(dFy/dx)^2 + (dFx/dy)^2]

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# I Intuitively understand the curl formula?

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