- #1

cianfa72

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- TL;DR Summary
- About the linearly independence of Maxwell's

PDE equations

HI,

consider the 4 Maxwell's equations in microscopic/vacuum formulation as for example described here Maxwell's equations (in the following one assumes charge density ##\rho## and current density ##J## as

Two of the equations are scalar (divergence based equations) while the other two give rise to 6 equations in 6 unknowns (curl based equations).

Therefore it seems there are 8 equations in 6 unknowns (##E## and ##B## field components).

Are the above partial differential equations (PDEs) actually linearly dependent ? Thanks.

consider the 4 Maxwell's equations in microscopic/vacuum formulation as for example described here Maxwell's equations (in the following one assumes charge density ##\rho## and current density ##J## as

*assigned*-- i.e. they are not unknowns but are given as functions of space and time coordinates).Two of the equations are scalar (divergence based equations) while the other two give rise to 6 equations in 6 unknowns (curl based equations).

Therefore it seems there are 8 equations in 6 unknowns (##E## and ##B## field components).

Are the above partial differential equations (PDEs) actually linearly dependent ? Thanks.

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