Current density: 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?

Question

Quizplus · Accepted Answer

The average 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 with diameter $d$ is $\pi(\frac{d}{2})^2$. For $d = 2.0 \, \text{mm} = 2.0 \times 10^{-3} \, \text{m}$, the area $A = \pi(1.0 \times 10^{-3})^2 = \pi \times 10^{-6} \, \text{m}^2$. Thus, $J = \frac{2.4}{\pi \times 10^{-6}} \approx 7.6 \times 10^5 \, \text{A/m}^2$, which matches choice A.

Current Density: If a Current of 2