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Identify the physical law represented by J = σ E, where J is current density, σ is electrical conductivity, and E is the electric field intensity.

Difficulty: Easy

Correct Answer: Ohm's law

Explanation:


Introduction / Context:
Material relations link field quantities to response variables. In conductors under steady, low-field conditions, current density is proportional to electric field. This constitutive relation is the differential (point) form of Ohm's law.


Given Data / Assumptions:

  • Uniform, isotropic conductor characterized by conductivity σ.
  • Quasi-static, ohmic conditions (no significant displacement current or nonlinear effects).
  • Relation: J = σ E.


Concept / Approach:
Ohm's law at a point states that the proportionality between J and E is σ. In integral form for a uniform conductor of length L and cross-section A, V = I R with R = L/(σ A), consistent with the differential statement.


Step-by-Step Solution:

Recognize J (A/m^2) and E (V/m) are linked by σ (S/m).Map to macroscopic Ohm's law: I = ∫J·dA and V = ∫E·dl.Recover V = I R with R = L/(σ A), confirming the identification.


Verification / Alternative check:

Dimensional check: (S/m)*(V/m) = A/m^2 matches J.


Why Other Options Are Wrong:

Gauss's law relates flux of E to charge; Ampère's law relates H to current; Biot–Savart gives magnetic field from currents; Faraday's law relates changing flux to induced emf.


Common Pitfalls:

Confusing constitutive relations with field (Maxwell) laws.


Final Answer:

Ohm's law
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