5. (a) Derive the formula for the magnetic field of an ideal long air-core solenoid carrying a current I (14)_______ (represented with I, the number of turns per unit length of this solenoid n, and permeability constant μ₀.). (b) Find the magnitude of the magnetic field at the center of the endpoint of a long solenoid (length l ＞＞ radius R). (also expressed with n, I, μ₀.) (15)_______ (c) If the current of the above-mentioned long solenoid increases at a rate of 200 A/s, and the number of coil turns per unit length n is 1000 turns; the radius of the solenoid R is 3.0 cm, then an aluminum alloy with a radius of 5.0 cm and a resistance of 0.0001 Ω is placed at the endpoint of this long air-core solenoid as shown in Figure 4. Approximately estimate the induced current in amperes? (16)_______.