Explanation of the Negative Sign in Maxwell's Equations for curl(E).

[Talanum46]

I can explain why Maxwell's Equations have a negative sign in the equation for curl(E). This is done with an extension of the definition of the determinant to Det_R (determinant developed by row) and Det_C (determinant developed by column) for non-square matrices. See the attached paper.

NxM determinant.pdf

[OceanBreeze]

The matrix/determinant math is impressive, is it your paper?

As impressive as it is, I find it too complex to glean any keen insights into the reason for the negative sign in Maxwell’s third equation, also known as Faraday's law of electromagnetic induction.

Personally, I find the field vector form to be far more intuitive, that is: ∇×E = −∂B/∂t

Here it can be immediately seen that the induced Electric vector field opposes changes in the generating magnetic field. The significance of the negative sign is that energy is conserved in the interaction of the Electric and Magnetic fields. (If the sign were positive, there would be a positive feedback leading to a runaway condition and COE would be violated)

Also, I freely admit I do not understand this (from the referenced paper):

“Equation (1) shows that: in a spatially varying magnetic potential such that the terms in (1) does not all cancell and some of it is non-zero and non-constant, time would flow faster or slower than a clock outside the potential.”

So, here is your teaching moment, Talanum, can you please explain the above quote in a way that even I can understand it?

[Talanum46]

There was an error. See attached paper.

 

NxM determinant.pdf

[Talanum46]

I thought, since the h-component is non zero relative time would be slower or faster, but I see now that you need a t' and t relation to conclude this.