A long solenoidal coil of length L has N turns in total,uniformly packed from inner radius a to outer radius b. (a) With a current I flowing in the coil, what is the current density J(r)? (b) Find the magnetic field B(r) (i) in the bore of the solenoid, (ii) within the coil, and (iii) outside the solenoid. (c) Due to a manufacturing error, the solenoid has a cross section that is not quite circular. Fortunately, the irregular cross section remains the same along the entire length of the solenoid. The length L and total number of turns N remain unchanged. i. Use symmetry to constrain the magnetic field B(r) as much as possible. (Write an ansatz.) ii. Do you have enough information to determine the magnetic field B(r) in the bore of the solenoid? If yes, do so. If not, constrain B(rwithin the bore as much as possible.

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