# 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 (m^{2}). This is a vector quantity, with both a magnitude (scalar) and a direction.

J = I/A

J = current density in amperes/m^{2}

I = current through a conductor, in amperes

A = cross-sectional area of the conductor, m^{2}

Current Density Formula Questions:

1) A current of 6 mA is flowing through a copper wire that has an area of 4 mm^{2}. 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 mm^{2} = 0.004 m^{2} (or 4 x 10^{-3} m^{2}). Use the equation for current density.

J = I/A

J = 0.006 amps/0.004 m^{2}

J = 1.5 amps/m^{2}

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

Answer: The current, I = 45 amps and the area A = 8 m^{2}.

J = I/A

J = 45 amps/8m^{2}

J = 5.63 amps/m^{2}

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