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.

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Solve this multiple-choice question and choose the correct option.

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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

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.

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