Non physical solutions of Maxwell’s equations

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Can someone give me examples of mathematical solution to the Maxwell’s equations that have no physical meaning?
 
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You are inside a conducting shell. Outside the shell is an infinite sea of charge (the unphysical part).
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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