If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm,what is the average current density in this wire? A) 7.6 × 10⁵ A/m² B) 5.2 × 10^-6 A/m² C) 1.9 × 10⁵ A/m² D) 3.6 × 10⁵ A/m² E) 21 × 10^-6 A/m²

Question

Quizplus · Accepted Answer

The current density $J$ is given by $J = \frac{I}{A}$, where $I$ is the current and $A$ is the cross-sectional area of the wire. The area $A$ of a cylindrical wire is $\pi r^2$, where $r$ is the radius of the wire. Given the diameter is 2.0 mm, the radius $r$ is 1.0 mm or $1.0 \times 10^{-3}$ m. Thus, $A = \pi (1.0 \times 10^{-3})^2 = 3.14 \times 10^{-6}$ m$^2$. The current $I$ is 2.4 A. Therefore, $J = \frac{2.4}{3.14 \times 10^{-6}} = 7.6 \times 10^5$ A/m$^2$.

If a Current of 2