Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 4

4 Nonuniform electric field. In Fig. 32-19, an electric field is directed out of the page within a circular region of radius \( R = 4.00 \text{ cm} \). The field magnitude is \( E = (0.500 \text{ V/m}\cdot\text{s})(1 - r/R)t \), where \( t \) is in seconds and \( r \) is the radial distance (\( r \le R \)). What is the magnitude of the induced magnetic field at radial distances (a) 2.00 cm and (b) 5.00 cm? (c) At what radial distance is the field magnitude maximum?