Question

The SI unit of the current density is 

Hint:

Current density (\( J \)) represents the electric current flowing per unit area of a conductor. Its SI unit is \( {A/m}^2 \).

Answer 1

Step 1: Understanding Current Density 
Current density (\( J \)) is defined as the electric current per unit area of cross-section: \[ J = \frac{I}{A} \] where:
- \( J \) is the current density,
- \( I \) is the electric current (in amperes),
- \( A \) is the cross-sectional area (in square meters). 
Step 2: SI Unit of Current Density 
- The SI unit of electric current (\( I \)) is ampere (A).
- The SI unit of area (\( A \)) is square meter (m\(^2\)).
- Thus, the SI unit of current density is: \[ J = \frac{{A}}{{m}^2} = {A/m}^2 \] 
Step 3: Importance of Current Density 
- Higher current density means a stronger electric field in a conductor.
- Used in Ohm's Law in differential form: \[ J = \sigma E \] where \( \sigma \) is conductivity and \( E \) is the electric field. Thus, the SI unit of current density is \( {A/m}^2 \).