Current Density Formula

In the field of electromagnetism, Current Density is the measurement of electric current (charge flow in amperes) per unit area of cross-section (m²). This is a vector quantity, with both a magnitude (scalar) and a direction.

J = I/A

J = current density in amperes/m²

I = current through a conductor, in amperes

A = cross-sectional area of the conductor, m²

Current Density Formula Questions:

1) A current of 6 mA is flowing through a copper wire that has an area of 4 mm². What is the current density?

Answer: The current through the conductor is I = 6 mA = 0.006 amperes (or 6 x 10^-3 amps). The area of the wire is A = 4 mm² = 0.004 m² (or 4 x 10^-3 m²). Use the equation for current density.

J = I/A

J = 0.006 amps/0.004 m²

J = 1.5 amps/m²

2) If 45 amperes of current is flowing through a battery with a given area of 8 m², what is the current density?

Answer: The current, I = 45 amps and the area A = 8 m².

J = I/A

J = 45 amps/8m²

J = 5.63 amps/m²