Your employer asks you to build a 27cmlong solenoid with an

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Your employer asks you to build a 27-cm-long solenoid with an interior field of 4.1 mT. The specifications call for a single layer of wire, wound with the coils as close together as possible. You have two spools of wire available. Wire with a #18 gauge has a diameter of 1.02 mm and has a maximum current rating of 6 A. Wire with a #26 gauge is 0.41 mm in diameter and can carry up to 1 A Which wire should you use? . #18 #26 Submit My Answers Give Up Correct Part B What current will you need? Express your answer to two significant figures and include the appropriate units Value Units Submit My Answers Give Up

Solution

note: post your questions seperately:

The magnetic field due to the solenoid:

                 B = ₀NI / L

current is,

I =   BL / ₀N

For (#18 guage ) wire:

            N = L / d =   0.27 / ( 1.02*10^-3)   = 264.7

hence the current is,

           I =   BL / ₀N = 4.1*10^-3*0.27/4*pi*10^-7*264.7 = 3.33 A

For #26 gauge wire :

Number of turns:

       N =L /d = 0.27 / (0.41 *10^-3m )   = 658.536 turns

hence, the current is,

        I =   BL / ₀N = 4.1*10^-3*0.27/ 4*pi*10^-7*658.536 = 1.338 A > 1A limit of the wire

therefore, I = 3.33 A for #18 guage wire is with in the limit of 6 A. thus, #18 guage wire is suitable