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I have a hard time understanding what the curl really means in Maxwell's equations, for example in a steady-state you have

[tex]\nabla\times \textbf{E} = 0[/tex]

and in a time-varying field you have

[tex]\nabla\times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}[/tex]

The meaning of the divergence is like "outflow - inflow". I read that the curl is like the amount of rotation. But what does it means in this situation with the electric field? That electric field lines don't "rotate"/curve like for the magnetic field?