Graduate Maxwell equation. Commuting time and spatial derivatives.

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The discussion focuses on the conditions under which the relation curl(-∂B/∂t) = -∂/∂t curl B can be applied. It emphasizes that partial derivatives of any field commute when all second partial derivatives are continuous functions. This is crucial for understanding the mathematical framework of Maxwell's equations in electromagnetism. The conversation highlights the importance of continuity in derivatives for the validity of this relation. Overall, the proper application of these mathematical principles is essential for accurate electromagnetic analysis.
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When we can use relation?
\mbox{curl}(-\frac{\partial \vec{B}}{\partial t})=-\frac{\partial}{\partial t}\mbox{curl}\vec{B}
 
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The partial derivatives of any field commute if all 2nd partial derivatives are continuous functions.
 

Thread 'What determines if wave components are independent vs coherent?'

I'm working through something and want to make sure I understand the physics. In a system with three wave components at 120° phase separation, the total energy calculation depends on how we treat them: If coherent (add amplitudes first, then square): E = (A₁ + A₂ + A₃)² = 0 If independent (square each, then add): E = A₁² + A₂² + A₃² = 3/2 = constant In three-phase electrical systems, we treat the phases as independent — total power is sum of individual powers. In light interference...
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