Problem 32.49 Your employer asks you to build a 23-cm-long solenoid with an inte
ID: 1460505 • Letter: P
Question
Problem 32.49 Your employer asks you to build a 23-cm-long solenoid with an interior field of 5.5 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. Part A Which wire should you use? #18 #26 Part B What current will you need? Express your answer to two significant figures and include the appropriate units. I=Explanation / Answer
A)
Let us 1st assume that we cover whole of solenoid with wire
When using #18:
Total number of turns, N = Total length / diameter = 230 mm / 1.02 mm = 225.5
B = N*miuo*I/L
=225.5 * (1.2566*10^-6)*6/0.23 {L = 23 cm = 0.23 m}
=7.4*10^-3 T
This is greater than 5.5 mT
When using #26:
Total number of turns, N = Total length / diameter = 230 mm / 0.41 mm = 561
B = N*miuo*I/L
=561 * (1.2566*10^-6)*1/0.23 {L = 23 cm = 0.23 m}
=3.06*10^-3 T
This is less than 5.5 mT
So #26 will not be able to provide 5.5 mT even at maximum current.
SO,
Answer is : # 18
B)
Let the current be I A
When using #18:
Total number of turns, N = Total length / diameter = 230 mm / 1.02 mm = 225.5
B = N*miuo*I/L
5.5*10^-3 =225.5 * (1.2566*10^-6)*I/0.23 {L = 23 cm = 0.23 m}
I = 4.5 A
Answer: 4.5 A
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