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# A 300-turn solenoid has a radius of 5.00 cm and a length of 20.0 cm. Find (a) the inductance of the solenoid and (b) the energy stored in the solenoid when the current in its windings is 0.500 A.

## a. 0.00444 Hb. 0.555 m J

### Discussion

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##### Andy C.

University of Michigan - Ann Arbor

##### Marshall S.

University of Washington

### Video Transcript

So, for our question, were given a solenoid that has 300 turns a radius of five centimeters, which I converted two meters 20.5 meters and the length of 20 centimeters or 200.2 meters, and for part a were asked to find the induct its well. The inductions, which is denoted as l is equal to the vacuum, your primitive ity of free space from you, not which is four pi times 10 to the minus seven constant. You can look up times the number of turns squared times the area divided by the length. Okay, so then this is unite times, the number of turns squared and in the area is pi r squared. We use capital are here for radius, so let's keep that consistent. Divided by the link. Plugging those values into this expression, we find that the induct in CE is 4.44 times 10 to the minus three Henry's, which is 4.44 Millie Henry's again 10 to the minus three. Henry's is Milly Henry's so we can destroy it as Miller Henry's. We'll box it in his air solution for a for part, B asked us to find the potential energy that's stored. Uh, when the current that is stored is equal to 0.5 amperes. Well, the potential energy that's stored from induct its use Our use of l is equal to 1/2 times the induction ce times the current square. So again, playing me in the value for the current that's stored here with 0.5 amperes and the value for induct in CE which we just found, we find it this comes out to be zero 0.555 And in the units here are Millet Jules Weaken box that it is their solution for part B.

University of Kansas
##### Andy C.

University of Michigan - Ann Arbor

##### Marshall S.

University of Washington