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This is a simulation of a two-dimensional electromagnetic wave. Such waves are predicted by Maxwells four equations, which we learned in the video about Maxwells equations. If we set charge density and the current density equal to zero, we get Maxwell equations whose solutions are valid only if there are no charges and currents in space. We get Maxwell equations in vacuum. These tell us the existence of electromagnetic waves in vacuum. How do we get the wave equations for the E- and B-field? The Maxwell equations are coupled differential equations, that means: The unknowns E and B are together in one equation, namely in the third and fourth Maxwell equation. Let us take Maxwells equation for the curl of the E-field and decouple it. To do this, we apply the cross product with the Nabla operator on both sides of the equation. The time derivative together with the minus sign may be placed in front of the Nabla operator, because the Nabla operator does not depend on time. Now you c