What is the physical interpretation of curl of curl of an E-field vector? I know that this gives the expression for an EM wave using the Maxwell equations but, I want to understand what exactly curl of curl signifies?

  • $\begingroup$ Are you interested in what physical quantity is represented (like electric or magnetic field or flux density), or how to intuitively understand the $\nabla \times \nabla \times$ operator (like how the second derivative of a 1D scalar function relates to the curvature)? $\endgroup$ – LedHead Jun 16 '17 at 6:51
  • $\begingroup$ Yes, I want to understand what does two times curl means? Why curl of a curl? $\endgroup$ – Pacifier Jun 19 '17 at 0:17

Curl actually signifies the rotation of a field(twice the angular frequency in fact).Curl of a curl according to me will signify how fast the curl is itself rotating.(I know it sounds weird).to get the EM wave equation ,we actually put the $\rho$ and J to be zero and use a mathematical trick to get to the equation.

  • $\begingroup$ Thanx Rishabh. I know the analytical way to get the wave equation, but still, I'm not convinced with the answer, maybe I'm not getting it. Could you please try to explain the curl of curl by taking any example? $\endgroup$ – Pacifier Jun 13 '17 at 4:08
  • $\begingroup$ en.wikipedia.org/wiki/Curl_(mathematics).I am sure that you have already visited this page.In the velocity example given here,you can see that the curl is fixed because the field is rotating uniformly at every point.if the field is something more complicated like $(x^2+y^2)\div 2 z\hat$ which is just a velocity field pointing in the z direction whose magnitude is increasing in proportion to distance^2,then it's curl will be same as the one given in the example here and its curl of curl will be fixed.you can see a point kept in the field will show a very complicated path . $\endgroup$ – Rishabh Jain Jun 13 '17 at 13:40

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