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Perfect Conductors.doc
Perfect Conductors
Consider now some current with density J(r ) , flowing within
some material with perfect conductivity (i.e., σ = ∞ )!
σ =∞
E(r ) = ??
J(r )
Q: What is the electric field E(r ) within this perfectly
conducting material?
A: Well, we know from Ohm’s Law that the electric field is
to the material conductivity and current density as:
E(r ) =
J(r )
Thus, as the material conductivity approaches infinity, we
lim E(r ) =
σ →∞
Jim Stiles
J(r )
The Univ. of Kansas
Dept. of EECS
Perfect Conductors.doc
The electric field in within a perfectly conducting material is
always equal to zero!
This makes since when you think about it! Since the material
offers no resistance, we can move charges through it without
having to apply any force (i.e., and electric field).
This is just like a skater
moving across frictionless
ice! I can continue to
move with great velocity,
even though no force is
being applied!
Consider what this means with regards to a wire made of a
perfectly conducting material (an often applied assumption).
The electric potential difference between either end of a
perfectly conducting wire is zero!
V = ∫ E (r ) ⋅d A = 0
Jim Stiles
Since the electric field
within a perfect wire is
zero, the voltage across
any perfect wire is also
zero, regardless of the
current flowing through it.
The Univ. of Kansas
Dept. of EECS