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Consider two EM waves, the first one moving the positive x-axis and the second one moving the positive y-axis such that the electric field component of the two EM wave is in the z-axis.

Let the electric field of the first wave be $z=E_1=E_{0}\sin(\omega t-kx)$ and the electric field of the second wave be $z=E_2=E_{0}\sin(\omega t-ky)$. enter image description here

We can see that the two waves meet at $(x,y)=(0,0)$. At this point $E_1+E_2=2E_{0}\sin(\omega t)$ so there is always constructive interference at $(x,y)=(0,0)$. The energy stored in a electric field is square of its amplitude so due to constructive interference energy becomes double at this point.

So my question is, as there is no destructive inteference where does this extra energy stored in the electric field due to constructive inteference come from?

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  • $\begingroup$ this MIT video might interest you, where it deals with laser beams interfering ocw.mit.edu/resources/… $\endgroup$
    – anna v
    Commented Mar 9, 2022 at 9:13
  • $\begingroup$ Hint: do electric waves exist on their own? :) $\endgroup$
    – jensen paull
    Commented Mar 9, 2022 at 10:48
  • $\begingroup$ @jensenpaull I have considered the effect of magnetic field. If the magnetic field amplitude of the two waves are equal say $B_0$, the resultant would be $\sqrt{2}B_0$(magnetic fields are perpendicular to each other), so there will be no change in the energy stored in the magnetic field. $\endgroup$
    – Asher2211
    Commented Mar 9, 2022 at 13:43
  • $\begingroup$ physics.stackexchange.com/questions/196650/… look at the accepted answer $\endgroup$
    – jensen paull
    Commented Mar 10, 2022 at 9:54

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