Current Density
Current density (J) is a vector quantity defined as the electric current per unit cross-sectional area perpendicular to the direction of current flow, given by J = I/A or J = nevd.
What is Current Density?
A vector quantity representing the electric current per unit area perpendicular to the direction of current flow.
Key formula / rule: Current Density (Area definition)
Key points
- Define current density and its vector nature.
- Derive the relationship between current density, current, and area.
- Express current density in terms of microscopic parameters (n, e, vd).
- Understand the SI unit of current density.
Common exam trap
Confusing current density with current (scalar vs. vector).
Definitions
- Term
Current Density
- Meaning
A vector quantity representing the electric current per unit area perpendicular to the direction of current flow.
- Term
Drift Velocity
- Meaning
The average velocity attained by charge carriers in a material due to an electric field.
- Term
Conductivity
- Meaning
A measure of a material's ability to conduct electric current, it is the reciprocal of resistivity.
Learning objectives
Define current density and its vector nature.
Derive the relationship between current density, current, and area.
Express current density in terms of microscopic parameters (n, e, vd).
Understand the SI unit of current density.
Relate current density to the electric field and conductivity.
Formulae
- Name
Current Density (Area definition)
- Note
Where I is the current and A is the cross-sectional area perpendicular to the current flow. J is a vector.
- Expression
J = I/A
- Name
Current Density (Microscopic definition)
- Note
Where n is the number of charge carriers per unit volume, e is the charge of each carrier, and vd is the drift velocity.
- Expression
J = nevd
- Name
Microscopic Ohm's Law
- Note
Where σ is the conductivity of the material and E is the electric field.
- Expression
J = σE
Prerequisites
Electric Current
Ohm's Law
Drift Velocity
Electric Field
Scalar and Vector Quantities
Common mistakes
Confusing current density with current (scalar vs. vector).
Assuming the area 'A' is always the total cross-sectional area without considering perpendicularity.
Incorrectly applying the formula J = nevd without understanding the terms 'n', 'e', and 'vd'.
Forgetting the vector nature of current density when dealing with non-uniform fields or complex geometries.
Keywords
Current Density
Electric Current
Area
Drift Velocity
Charge Carriers
Conductivity
Vector Quantity
Microscopic Ohm's Law
Practice preview
If a current of 10 A flows through a wire with a cross-sectional area of 5 x 10⁻⁶ m², what is the current density?…
easy
A current of 2 A flows through a wire of cross-sectional area 1 mm². Calculate the current density.…
medium
What is the SI unit of current density?…
easy