Your employer asks you to build a 36-cm-long solenoid with an interior field of

Question

Your employer asks you to build a 36-cm-long solenoid with an interior field of 5.4 mT. The specifications call for a single layer of wire, wound with the coils as close together at possible. You have two spools of wire available. Wire with a # 18 gauge hat 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? #26 #18 What current will you need? Express your answer to two significant figures and include the appropriate units. I =

Explanation / Answer

Hi,

Please find the below solution.

B = µ0 X N /( L X I )
µ0 = 4 10^-7
N = 350 mm / 1.02 = 343.13 turns
B = 4 10^-7 * 343.13/ 0.35 * I
5.4 x 10^-3 = 4 x 10^-7 x 980.39 x I
I = 5.9 10^-3 / 4 10^-7 * 980.39

= 5.9 10^-3 / 12324.9 10^-7

= 4.787 A

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