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

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The discussion centers on the relationship between the curl of the magnetic field and current density in electromagnetism. The user questions whether the equation del x dB/dt = mu dJ/dt holds true given del x B = mu J. A response confirms that this equality is valid because derivatives with respect to independent variables can be interchanged. The clarification helps the user understand the reasoning behind the equation. Overall, the conversation emphasizes the commutative property of derivatives in the context of electromagnetic equations.
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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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