Learning Goal: To learn about self-inductance from the example of a long solenoid. To explain self-inductance, it is helpful to consider the specific example of a long solenoid, as shown in the figure. This solenoid has only one winding, and so the EMF induced by its changing current appears across the solenoid itself. This contrasts with mutual inductance, where this voltage appears across a second coil wound on the same cylinder as the first. (Figure 1) Assume that the solenoid has radius R, length Z along the z axis, and is wound with n turns per unit length so that the total number of turns is equal to nz. Assume that the solenoid is much longer than its radius. As the current through the solenoid changes, the resulting magnetic flux through the solenoid will also change, and an electromotive force will be generated across the solenoid according to Faraday's law of induction: fE-di-- M(1) Faraday's law implies the following relation between the self-induced EMF across the solenoid and the current passing through it: 8(t)=L() The "direction of the EMF is determined with respect to the direction of positive current flow, and represents the direction of the induced electric field in the inductor. This is also the direction in which the "back-current" that the inductor tries to generate will flow. Figure Air-Core Solenoid Schematic Symbol B 1 of 1 > Part A Suppose that the current in the solenoid is I (t). Within the solenoid, but far from its ends, what is the magnetic field B (t) due to this current? Express your answer in terms of I (t), quantities given in the introduction, and relevant constants (such as po). B (t) = Submit Part B 1 (t)= What is the magnetic flux 1 (t) through a single turn of the solenoid? Express your answer in terms of the magnetic field B (t), quantities given in the introduction, and any needed constants. ▾ Part C Request Answer Submit Request Answer &= Submit Be ▾ Part D 10 6 17. Suppose that the current varies with time, so that dI(t)/dt0. Find the electromotive force & induced across the entire solenoid due to the change in current through the entire solenoid. Express your answer in terms of di(t)/dt, n, Z, and R. View Available Hint(s) 4 (0 63 17 - Now + Review I Constants 1017 - The self-inductance L is related to the self-induced EMF & (t) by the equation 8(t)--LdI(t)/dt Find L for a long solenoid. (Hint: The self-inductance I will always be a positive quantity.)