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) What is the magnetic field outside the solenoid?

(c) The current is changing with time, so that the magnetic field changes with time. Sketch the solenoid and add electric field lines to your sketch.

(d) Carefully choose an appropriate loop with which to apply Faraday's law and indicate your loop on your sketch.

(e) Use your loop from (d) to calculate the electric field for values of the radial coordinate, r, for which r < a in terms of di/dt . What is the direction of the electric field?

(f) Now, calculate the electric field for values of the radial coordinate, r, for which a < r < b in terms of di/dt .