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10/25/2005 Perfect Conductors.doc 1/2 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 ) σ Thus, as the material conductivity approaches infinity, we find: lim E(r ) = σ →∞ Jim Stiles J(r ) σ The Univ. of Kansas =0 Dept. of EECS 10/25/2005 Perfect Conductors.doc 2/2 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 C 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