Your employer asks you to build a 32-cm-long solenoid with an interior field of

Question

Your employer asks you to build a 32-cm-long solenoid with an interior field of 5.2 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

B = µ ° N / L * I
µ° = 4 10^-7
N = 320 mm / 1.02 = 313.72 turns
B = 4 10^-7 * 313.72 / 0.32 * I
5.2 *10^-3 = 4 10^-7 * 980.37 * I
I = 5.2 10^-3 / 4 10^-7 * 980.37 = 4.22 A ( 6A)

Wire with a #18 gauge has a diameter of 1.02mm --- 313.72 turns ( 30.7cm)
I = 4.22 A---- B = 0.005900274 T = 5.2 mT

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