What is the current density in a copper wire having a radius

What is the current density in a copper wire having a radius of 1.00 mm and carrying a current of 1.00 mA? What is the drift speed of the electrons carrying this current? The density of copper is 8.96 middot 10^3 kg/m^3, and 1 mole of copper has a mass of 63.55 g. There is one conduction electron per atom is copper.

Solution

Current density=I/A

Area=3.14×10⁶ m² (A = × (0.001 m)²).

J=0.001/(3.14×10⁶ )

J=318.47 A/m²

Copper has a density of 8.96 g/cm³, and an atomic weight of 63.55 g/mol, so there are 140991.34 mol/m³. In one mole of any element, there are 6.02×10²³ atoms (Avogadro\'s constant). Therefore, in 1 m³ of copper there are about 8.49×10²⁸ atoms (6.02×10²³ × 140991.34 mol/m³). Copper has one free electron per atom, so n is equal to 8.49×10²⁸ electrons per cubic metre.

A current I = 0.001 ampere, and a wire of 2 mm diameter (radius = 0.001 m). This wire has a cross-sectional area of 3.14×10⁶ m² (A = × (0.001 m)²). The charge of one electron is q = 1.6×10¹⁹ C. The drift velocity therefore can be calculated:

u=I/nAq

u=(0.001)/[(8.49×10²⁸)(3.14×10⁶)(-1.6×10¹⁹)]

u=2.34x10⁸ m/s