Problem 3: Toroidal Solenoid A toroidal solenoid of rectangular cross-section has inner radius a, outer radius b, height c, and has N turns. In this problem, c >> a and c >> b. The current in the solenoid is i(t) at time t . (a) What is the magnetic field B(r) inside the solenoid as a function of radial position r from the symmetry axis of the solenoid? $ B . dl = Ho Enc B : the magnetic field strength, 40 : the permeability of free space (4xx10-7T.m/A). In the solenoid, the magnetic fields travel a circular path. So B (2ur) = Hoene 1 = Ni(t) B(2ntr) = U Ni(t) H Ni(t) inside = 2ur (b) What is the magnetic field outside the solenoid? When r b, the magnetic field is zero. This is because the toroidal solenoid's design ensures that the magnetic field lines are contained entirely within the solenoid, with no field lines escaping outside. B outside = 0(e) Use your loop from (d) to calculate the electric field for values of the radial coordinate, r, for which r