Law

Ohm's law

J = σ E

Statement

In an ohmic material the current density is proportional to the applied field, with conductivity σ as the constant.

Symbols and units

$J$	current density	A/m²
$σ$	conductivity of the material	(Ω·m)⁻¹
$E$	field inside the material	V/m

When it applies

Ohmic materials only — not diodes, gas discharges or filament lamps.

Don't use when

A material property, not a universal law — fails for diodes, gas discharges, and filament lamps, where resistance depends on voltage or current.

Derivation

Experimental observation for many materials: doubling the field doubles the flow.

J \propto E

Name the constant of proportionality:

J = σ E

Resistivity is its inverse:

ρ = \frac{1}{σ}

Watch out for

This is a property of certain materials, not a law of nature — it fails for gases, semiconductor junctions and filament lamps.

Connects to