A long solenoid with self-inductance L and radius r is connected to an AC voltage source with frequency ω and max voltage V. Then a thin cylindrical shell with the same length and the same cross-section area with the solenoid is inserted into middle of the solenoid without touching it. It has thickness δ (δ<<r) and resistivity ρ.
Ignore resistance of the solenoid. No current between the solenoid and the cylinder.
Proof that this system is equal to a system where the solenoid is in series with a resistor! Determine the resistance R of this resistor! Assume the system is in vacuum.
Also assume that magnetic field inside the solenoid and the cylinder is uniform and equals to magnetic field at the middle.
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