Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 20

20 Figure 32-22a shows the current i that is produced in a wire of resistivity $1.62 \times 10^{-8} \text{ }\Omega\cdot\text{m}$. The magnitude of the current versus time t is shown in Fig. 32-22b. The vertical axis scale is set by $i_s = 10.0 \text{ A}$, and the horizontal axis scale is set by $t_s = 50.0 \text{ ms}$. Point P is at radial distance $6.00 \text{ mm}$ from the wire's center. Determine the magnitude of the magnetic field $\vec{B}$ at point P due to the actual current i in the wire at (a) $t = 20 \text{ ms}$, (b) $t = 40 \text{ ms}$, and (c) $t = 60 \text{ ms}$. Next, assume that the electric field driving the current is confined to the wire. Then determine the magnitude of the magnetic field $\vec{B}_{id}$ at point P due to the displacement current $i_d$ in the wire at (d) $t = 20 \text{ ms}$, (e) $t = 40 \text{ ms}$, and (f) $t = 60 \text{ ms}$. At point P at $t = 20 \text{ s}$, what is the direction (into or out of the page) of (g) $\vec{B}$ and (h) $\vec{B}_{id}$?