Current density

Definition

Current density is a measure of the electric current per unit area of cross-section in a material. It is typically denoted by the symbol $\mathbf{J}$ and has units of amperes per square meter ($A/m^2$).

5 Must Know Facts For Your Next Test

1. Current density $\mathbf{J}$ is calculated using the formula $\mathbf{J} = \frac{I}{A}$, where $I$ is the current and $A$ is the cross-sectional area.
2. It is a vector quantity, meaning it has both magnitude and direction.
3. High current density can lead to overheating and damage in conducting materials due to increased resistive heating.
4. In metals, current density is directly proportional to the electric field applied, following Ohm's Law in its microscopic form: $\mathbf{J} = \sigma \mathbf{E}$, where $\sigma$ is the electrical conductivity.
5. Current density plays a crucial role in determining the efficiency and safety of electrical circuits and devices.

Review Questions

• What formula is used to calculate current density?
• Why is current density considered a vector quantity?
• How does high current density affect conducting materials?

Related terms

Electric Current:

The flow of electric charge through a conductor, typically measured in amperes (A).

Electrical Conductivity: A measure of a material's ability to conduct an electric current, denoted by $\sigma$.

Ohm's Law:

$V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance; describes the relationship between voltage, current, and resistance.