26.3:
Current Density
Current density is the total amount of current flowing per unit cross-sectional area, measured in amperes per square meter.
When a small current flows through an infinitesimal area, a relationship between the current and the current density can be established, where theta is the angle between the area and the current density. Therefore, the total current passing through the area can be determined by integrating it over the area.
Consider the magnitude of the current density and recall the equation of drift velocity. By substituting the terms, a relation between current density and drift velocity can be established. While current is a scalar quantity, current density is a vector quantity.
Consider a current of 0.5 amperes flowing through a 50-watt bulb. The bulb is wired using a copper wire with a radius of 1.25 mm. Determine the magnitude of the current density.
The known values are the current and cross-sectional area, whereas the current density is an unknown quantity. By substituting the known quantities into the equation, the current density can be determined.
26.3:
Current Density
The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net flow of positive charges through the area. Also, for any given current, as the diameter of the wire in a circuit increases, the charge density decreases. The magnitude of the current density is the current divided by the area.
Thus, the current density can be determined as:
If q is positive, drift velocity is in the same direction as the electrical field. If q is negative, drift velocity is in the opposite direction to the electric field. Either way, the direction of the current density is in the direction of the electrical field. For example, in a sodium chloride solution, current can be carried by both positive sodium ions and negative chlorine ions; the total current is found by adding up the currents due to each kind of charged particle.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 394 – 396. Retrieved from https://openstax.org/books/university-physics-volume-2/pages/9-2-model-of-conduction-in-metals