- #1

Maxicl14

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**Summary::**There seems to be a mismatch, in the "Maxwell's" equations, between the number of equations and number of variables.

I was trying to play around with the equations for Electromagnetism and noticed something unusual. When expanded, there are 8 equations, 6 unknown variables, and 4 parameter variables. When the parameter variables are set using 4 more equations, the result is 10 variables and 12 equations. This seems 2 equations too many.

The variables I am referring to:

Ex, Ey, Ez, Bx, By, Bz,

x, y, z, t

The equations I am referring to:

1 from divergence of E

1 from divergence of B

3 from curl of E

3 from curl of B

4 from setting parameters: x=X, y=Y, z=Z, t=T.To give an example, the simple harmonic equations may be:

(d2/dt2) X(t) = -X(t)

t = T

This results in a unique solution of X (at t=T). 2 equations. 2 variables. Unique solution.

So why do Maxwell's equations behave differently, or do they? May it be to do with initial conditions? May some equations imply others?

Thank you, Max.