FIGURE P31.39 shows the electric field inside a cylinder

Chapter 31, Problem 31.65

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FIGURE P31.39 shows the electric field inside a cylinder of radius R = 3.0 mm. The field strength is increasing with time as E = 1.0 * 108 t 2 V/m, where t is in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for t 6 0. a. Find an expression for the electric flux e through the entire cylinder as a function of time. b. Draw a picture showing the magnetic field lines inside and outside the cylinder. Be sure to include arrowheads showing the fields direction. c. Find an expression for the magnetic field strength as a function of time at a distance r 6 R from the center. Evaluate the magnetic field strength at r = 2.0 mm, t = 2.0 s. d. Find an expression for the magnetic field strength as a function of time at a distance r 7 R from the center. Evaluate the magnetic field strength at r = 4.0 mm, t = 2.0 s.