Question

Ohm’s law relates the current density \( J \) with field intensity \( E \) as _______.

• A. \( J = \sigma E \)
• B. \( J = \frac{E}{\sigma} \)
• C. \( J = \rho E \)
• D. \( J = \sigma E^2 \)

Hint:

Microscopic Ohm’s Law → \( J = \sigma E \). Direct proportionality between current density and field!

Answer 1

The Correct Option is A

Step 1: Basic Ohm’s Law in Vector Form
Ohm’s law in microscopic form (point form) is: \[ J = \sigma E \] Where:
- \( J \) = current density (A/m²)
- \( E \) = electric field intensity (V/m)
- \( \sigma \) = conductivity of material (S/m)
Step 2: Why This Relation Holds
In a conductive medium, the current density is directly proportional to the electric field applied, with the constant of proportionality being the electrical conductivity.
Step 3: Clarify Other Options
- \( J = \frac{E}{\sigma} \) → incorrect, that's resistance relation.
- \( J = \rho E \) → wrong; resistivity \( \rho = \frac{1}{\sigma} \).
- \( J = \sigma E^2 \) → physically incorrect, not linear.
Conclusion:
Option (1) is correct — it correctly represents the microscopic form of Ohm’s Law.