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Curent Density inside perfect conductors

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dzafar

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Hi there,

I understand that conductivity σ, inside a perfect conductor approaches ∞. Also, E-field, inside as well as on the surface of PEC is 0.

Then according to Ohm's Law: J = σE what should the current density, J be inside the PEC, in this case?

J = ∞.0 ⇒ J = ? (0 or ∞ or something else?)

Thanks
 

J can have any value.

A superconductor can support any DC current with zero potential. However, you are ignoring the effects of the magnetic field produced by the DC current that will have an effect on the current.
 

So you mean in the case I provided, J will have a random value? I am just concerned about this specific case when J = ∞.0!

Thanks
 

We call it undetermined value; ∞ is not a number and you need to consider this as a limiting case. The current density will be determined by other considerations and not from this equation because according to the equation J will "undetermined" value.
 

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