Current density

The volume current density $⃗ 𝐉 : A \cdot m - 2$ is a vector density defined as

⃗ 𝐉 = 𝜌 + ⃗ 𝐯 + + 𝜌 - ⃗ 𝐯 -

where

$𝜌 \pm$ is the charge density restricted to positive or negative charges respectively.
$⃗ 𝐯 \pm$ is the velocity field of of positive or negative charges respectively.

The current $đ 𝐼$ through a surface element $𝑑 ⃗ 𝐚$ is then

𝑑 𝐼 = ⃗ 𝐉 \cdot 𝑑 ⃗ 𝐚

Properties

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