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breckenridgeback t1_jdygypz wrote

Reply to comment by PerturbedHamster in ELI5: Why are the Electric field and magnetic field always perpendicular to each other? by No_Victory_1611

> To (over)simplify the math, the curl of a thing is perpendicular to the thing

That is not true.

For example, if F is the vector field sin(x) i + 3 k, we have:

  • curl(F) = cos(x) k
  • F dot curl(F) = 3cos(x) != 0.

Nonzero dot product -> not perpendicular.

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PerturbedHamster t1_jdz002w wrote

I know it's not true in general, that's why I said it's an oversimplification. Given we're explaining vector calculus to a five year old, though, I thought it would be OK. What is true, though, is that if a vector field only has a single component then the curl does have to be perpendicular to the field. That's what's going on with linearly polarized light, and why I didn't feel too bad about oversimplifying.

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