A Maxwell equation. Commuting time and spatial derivatives.

LagrangeEuler
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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 'Inducing EMF Through a Coil: Understanding Flux'

Thread 'Inducing EMF Through a Coil: Understanding Flux'

Thank you for reading my post. I can understand why a change in magnetic flux through a conducting surface would induce an emf, but how does this work when inducing an emf through a coil? How does the flux through the empty space between the wires have an effect on the electrons in the wire itself? In the image below is a coil with a magnetic field going through the space between the wires but not necessarily through the wires themselves. Thank you.
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Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
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