At the instant when t$($a$)$ A long, straight solenoid has turns, uniform cross$-$sectional area and length Show that the inductance of this solenoid is given by the equation Assume that the magnetic field is uniform inside the solenoid and zero outside. $($Your answer is approximate because is actually smaller at the ends than at the center. For this reason, your answer is actually an upper limit on the inductance.$)($b$)$ A metallic laboratory spring is typically $5\mathrm{.}00$ cm long and $0\mathrm{.}150$ cm in diameter and has $50$ coils. If you connect such a spring in an electric circuit, how much self$-$inductance must you include for it if you model it as an ideal solenoid?he current in an inductor is increasing at a rate of the magnitude of the self$-$induced emf is $0\mathrm{.}0160$ V$.($a$)$ What is the inductance of the inductor? $($b$)$ If the inductor is a solenoid with $400$ turns, what is the average magnetic flux through each turn when the current is $0\mathrm{.}720$ A$?$