Maxwells derivation for speed light

AI Thread Summary
Maxwell's derivation of the speed of light is rooted in his equations, which describe electromagnetic waves. The speed of light can be derived from the wave equation that emerges from these equations. This derivation shows that light behaves as an electromagnetic wave, with its speed determined by the electric and magnetic constants. The mathematical relationship allows for the speed of light to be calculated directly from these constants. Understanding this connection highlights the fundamental nature of light in the context of electromagnetism.
NeilWallace
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Hi could someone help me understand maxwells reasoning for how to derive the speed of light and why it should be the velocity that it is?
 
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I think he based his math off of measurements on the speed of light. But I'm not certain.
 

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
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Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
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