A cylindrical solenoid of radius R and height h consists of N windings. There is a current through the windings, and this current increases with time as I=αt, where α is a constant. b. Determine the magnitude of the Poynting vector at a radial distance r=R from the center of the long center axis of the solenoid. Express your answer in terms of magnetic constant μ0, α, R, h, N and t. c. Use the result of the previous part to derive an expression for the power input to the solenoid as a function of time. Express your answer in terms of π, magnetic constant μ0, α, R, h, N and t. d. Using the formula for the inductance of an ideal solenoid, calculate the power from the rate of change of the stored magnetic energy. Express your answer in terms of π, magnetic constant μ0, α, R, h, N and t.

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