Why maxwell's 3rd equations has no coefficient?

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Maxwell's third equation, Faraday's Law, uniquely has a proportionality coefficient of -1, unlike the other three equations, which include constants due to differing units for electric field (E) and magnetic field (B). The absence of a coefficient in the third equation is attributed to the choice of units, particularly in Gaussian units where E and B are measured in the same units. The introduction of dimensional constants in the other equations arises from the need to reconcile these different units. This historical context reflects the evolution of measurement systems in physics. Understanding these unit choices clarifies why the third equation stands apart in its formulation.
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For the four Maxwell equations, only the third one (Faraday's Law) has a proportionality coefficient of -1, while rest have a magnetic constant or electric constant .

It doesn't seem like the units of the third law are calibrated to eliminate the constant. So why is the coefficient equal to exactly -1, not some materially dependent coefficient k?
 
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I second jasonRFs comment. It is purely due to the units chosen.
 
The real question is, why do the other 3 equations have dimensional constants introduced. That is because they use different units for E and B, even though they are parts of the same tensor.
 
Meir Achuz said:
The real question is, why do the other 3 equations have dimensional constants introduced. That is because they use different units for E and B, even though they are parts of the same tensor.

But this is historical - like measuring distances and times in different units. Time should be measured in meters.
 
Meir Achuz said:
The real question is, why do the other 3 equations have dimensional constants introduced. That is because they use different units for E and B, even though they are parts of the same tensor.

This is the answer I am looking for.
 
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