Question

For a research project, a student needs a solenoid that produces an interior magnetic field of 0.0100 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 17.0 cm long. Determine the number of layers of wire needed. (Round your answer up to the nearest integer.) Determine the total length of the wire. (Use the integer number of layers and the average layer diameter.)

The number of layers of wire needed is 4, but I can't figure out the total length of the wire.

Answer 1

Answer:

4

Explanation:

$\mu_0$ = Vacuum permeability = $4\pi \times 10^{-7}\ H/m$

d = Diameter = 0.5 mm

B = Magnetic field = 0.01 T

i = Current = 1 A

Number of layers is given by

$n=\dfrac{Bd}{\mu_0i}\\\Rightarrow n=\dfrac{0.01\times 0.5\times 10^{-3}}{4\pi \times 10^{-7}\times 1}\\\Rightarrow n=3.97887\ layers\approx 4$

So the number of layers is 4