Your employer asks you to build a 22-cm-long solenoid with an interior field of

Question

Your employer asks you to build a 22-cm-long solenoid with an interior field of 6.0 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?

What current will you need?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Lets calculate the current

B = µ ° N / L * I
µ° = 4 10^-7
N = 220 mm / 1.02 = 216turns
B = 4 10^-7 * 216 / 0.22 * I
6*10^-3 = 4 10^-7 * 980.39 * I
I = 6* 10^-3 / 4 10^-7 * 980.39 = 5.9 10^-3 / 12313 10^-7 = 4.872 A which is 6A

Hence , we go with a #18 gauge having a diameter of 1.02 mm

Current needed is 4.872 A

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