Solving Del Cross Question: Why is del x dB/dt = mu dJ/dt?

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SUMMARY

The discussion centers on the mathematical relationship between the curl of a magnetic field and the current density in electromagnetic theory, specifically addressing the equation del x B = μJ. Participants confirm that the equality del x dB/dt = μ dJ/dt holds true due to the commutativity of derivatives with respect to independent variables. This principle allows for the interchange of the order of differentiation, affirming the validity of the equation in the context of electromagnetic fields.

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  • Familiarity with electromagnetic theory, particularly Maxwell's equations.
  • Knowledge of partial derivatives and their properties.
  • Basic grasp of the concepts of magnetic fields and current density.
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Students and professionals in physics, particularly those studying electromagnetism, as well as educators looking to clarify concepts related to vector calculus and electromagnetic theory.

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Homework Statement


I have to do an E&M problem, I think I got it, but I made a few steps that I don't really understand. The first one is:

If delxB= muJ
Does
del x dB/dt = mu dJ/dt ??
If so, why ?

I tried using latex, but it didn't work...sorry :(


Homework Equations





The Attempt at a Solution

 
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hi miew! :smile:

(have a del: ∇ and a curly d: ∂ and a mu: µ :wink:)

yes, because derivatives wrt independent variables always commute (ie you can always change the order) …

∂2/∂x∂t = ∂2/∂t∂x :wink:
 
Thanks ! that makes sense :)
 

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