Electron current density, usually denoted by J, represents the amount of electric current flowing per unit area due to the movement of electrons. There are a few ways to determine it, depending on the information available.
1. Using Total Current and Area:
The most straightforward method is using the relationship between current density (J), total current (I), and cross-sectional area (A):
J = I / A
Where:
- J is the current density (typically in Amperes per square meter, A/m2)
- I is the total current flowing through the conductor (in Amperes, A)
- A is the cross-sectional area through which the current is flowing (in square meters, m2)
Example: If a wire carries a current of 2 Amperes and has a cross-sectional area of 0.5 square millimeters (0.5 x 10-6 m2), the current density would be:
J = 2 A / (0.5 x 10-6 m2) = 4 x 106 A/m2
2. Using Electron Drift Velocity and Charge Carrier Density:
Another way to calculate electron current density involves the electron drift velocity (vd), the number density of charge carriers (n), and the elementary charge (e):
J = n e vd
Where:
- J is the current density (in A/m2)
- n is the number of charge carriers (electrons) per unit volume (in m-3)
- e is the elementary charge (approximately 1.602 x 10-19 Coulombs)
- vd is the average drift velocity of the electrons (in m/s)
This formula highlights the microscopic origin of current density. A higher concentration of charge carriers or a faster drift velocity will result in a larger current density.
Example: If a copper wire has a charge carrier density of 8.49 x 1028 electrons/m3 and the electrons have a drift velocity of 1 x 10-4 m/s, the current density would be:
J = (8.49 x 1028 m-3) (1.602 x 10-19 C) (1 x 10-4 m/s) ≈ 1.36 x 106 A/m2
3. In terms of Conductivity and Electric Field:
Ohm's Law in its microscopic form relates current density to the electric field (E) and conductivity (σ):
*J = σ E**
Where:
- J is the current density (in A/m2)
- σ is the conductivity of the material (in Siemens per meter, S/m)
- E is the electric field strength (in Volts per meter, V/m)
This formulation is particularly useful when analyzing current flow in materials with varying conductivity or in situations where the electric field is known.
Example: If a material has a conductivity of 5.96 x 107 S/m and is subjected to an electric field of 0.02 V/m, the current density would be:
J = (5.96 x 107 S/m) * (0.02 V/m) = 1.192 x 106 A/m2
In summary, you can determine the electron current density using different formulas depending on the information available: total current and area, drift velocity and charge carrier density, or conductivity and electric field.
