7.1 cylindrical fields oscillating in time in a certain cylindrical region of space with radius r there is a time-varying homogenous field parallel to the the z-axis, which is also the axis of the cylinder. for example, you can assume that the field oscillates in time at a fixed frequency. it is therefore proportional to cos(ωt) assume that the field is either an electric field e(t) or a magnetic field b(t). in each case, describe the time- and space-dependence of the magnitude and direction of the field that is created inside and outside the cylinder. use r to indicate the distance from the axis of the cylinder. for a cylindrical electric field e(t): 1. derive an expression for b(r, t) for r < r. 2. derive an expression for b(r, t) for r > r. for a cylindrical magnetic field b(t): 3. derive an expression for e(r, t) for r < r. 4. derive an expression for e(r, t) for r > r