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A solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75 mV.

a. 0.002 H

b. -37.5 A / s

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Okay, So for poor Kay, we, uh is this equation productions, which is conducting sickles. You're not the permeability. Constant times a number of loops squared. Uh, times air. Rewrite that and squared times a over, Uh, l blinks. So we're just plugging in various for this first part. You, Not this four pi times 10 to the minus seven in the side units. Number of loop says 400 square that on and multiplied by area, which is pi r squared are as 0.25 meters. All right, so that's the That's the whole thing there. Divided by Twentys meters. 20 centimeters supporting two meters. This gives you permission. Our inductive off about two times to omega three hurt Henry's which is which is to Millie. Henry. Um, you know, it's so that's part a and part B. Ah has you using this equation? Ah m f is equal to induct ins times rate of change of current. So rate of change of current. It's just, uh, your mouth over induct in ce. So that's, uh, 75 million volts a 750.75 volts over two times 10 of the negatives. Three, uh, Henry's and This gives you, uh, current rate of change of current of about 38 amperes for a second, and that's it.