Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 7

7 Nonuniform displacement-current density. Figure 32-19 shows a circular region of radius \( R = 4.00 \text{ cm} \) in which a displacement current is directed out of the page. The magnitude of the density of this displacement current is \( J_d = (4.00 \text{ A/m}^2)(1 - r/R) \), where \( r \) is the radial distance (\( r \le R \)). What is the magnitude of the magnetic field due to the displacement current at (a) \( r = 2.00 \text{ cm} \) and (b) \( r = 5.00 \text{ cm} \)? (c) At what radial distance is the field magnitude maximum?