Violate current conservation in Perfect Magnetic Conductor (PMC)

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The discussion centers on the violation of current conservation in Perfect Magnetic Conductors (PMC) when electric currents are present. The original poster seeks clarification on why textbooks assert that electric currents should be zero in PMCs, expressing difficulty in proving this through boundary conditions or Lorentz force considerations. A question is raised about the specific type of current conservation being referenced, particularly whether the incoming and outgoing currents in a given volume are unequal. Additionally, there is curiosity about which parameters in PMC are considered infinite, drawing a comparison to Perfect Electric Conductors (PEC). The conversation highlights a gap in understanding regarding the behavior of electric currents in PMCs.
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Homework Statement
Why does having an electric current in Perfect Magnetic Conductor (PMC) violate current conservation?
Relevant Equations
Boundary conditions
Hello,
I need to know why having an electric current in Prefect Magnetic Conductor(PMC) violate current conservation. Based on the boundary conditions or lorentz force or ..., I couldn't be successful to prove that surface current can violate current conservation. In the textbooks, they mentioned the electric current should be zero but none of them explain it.

Thanks
 
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What type of current conservation are you talking about? Are you saying that for some volume, ##I_{in} \neq I_{out}## ?
 
Thanks berkeman,
Regarding this web page, I am curious to know why the electric currents should be zero.
In addition, which parameter in PMC is infinite( for example for perfect electric conductor(PEC) the conductivity (sigma) is infinite).
 

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