For a research project, a student needs a solenoid that produces an interior mag

Question

For a research project, a student needs a solenoid that produces an interior magnetic field of 0.0300 T. She decides to use a current of 1.00 A and a wire 0.500 mm in diameter. She winds the solenoid in layers on an insulating form 1.00 cm in diameter and 19.0 cm long.

a) Determine the number of layers of wire needed.(layers)

b) Determine the total length of the wire.(meters)(Use the integer number of layers and the average layer diameter.)

I have part (a) solved out with 12 layers.

I am stuck on part (b) having already tried answers 142.5m, 143.2m, 120m, 185m, 210m, 224m. The answer is within 10% of the 210m and 224m answers.

Explanation / Answer

Suppose,

No. of layers are = 12

Length of solenoid = 19 cm = 0.190 m

Solenoid diameter = 1 cm = 0.01 m

Wire diameter = 0.500 mm= 0.0005 m

Turns per layer = (length of solenoid/wire diameter )= (0.190/0.0005) = 380

Therefore,

Length of the wire = *(solenoid diameter)*(no. of turns per layer)*(No. of layers)

= 3.14 *0.01*380*12 = 143.18 m

Approximately,

Length of the wire is 143 meter.

By using all information and formula. The answer is 143 cm

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