Question

An 18-gauge copper wire (diameter 1.02 mm) carries a current with a current density of 1.40×10⁶ A/m2 . Copper has 8.5×1028 free electrons per cubic meter

Calculate the current in the wire

Calculate the drift velocity of electrons in the wire.

Answer 1

current density \(J=\frac{I}{A}=\frac{I}{\pi r^{2}}\)

\(r=\) radius \(=\frac{1.02 \mathrm{~mm}}{2}=0.51 \mathrm{~mm}=0.51 \times 10^{-3} \mathrm{~m}\)

current \(I=J A=J \pi r^{2}=1.4 \times 10^{6} \times p i \times\left(0.51 \times 10^{-3}\right)^{2}=1.14 A\)

drift velocity \(v_{d}=\frac{J}{n e}\)

drift velocity \(=v_{d}=\frac{1.4 \times 10^{6}}{8.5 \times 10^{28} \times 1.6 \times 10^{-19}}\)

\(v_{d}=0.103 \times 10^{-3} \mathrm{~m} / \mathrm{s}=0.103 \mathrm{~mm} / \mathrm{s}\)