Question

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 14 cm in diameter and 60 cm in length. You would like a 2.2 A current to produce a 2.5 kG magnetic field inside your solenoid.
What is the total length of wire you will need to meet these specifications?

L = km

Answer 1

Answer:

23.9Km

Explanation:

The following data are given

diameter, d =14cm =0.14m

r=d/2=0.07m

length,l=60cm

current,i=2.2A

magnetic field of 2.5kG we convert to telsa

$1 Gauss=10^{-4}T\\hence \\2500G=2500*10^{-4}\\0.25T$

First we determine the total number of turns from

$B=\frac{U_{0}NI}{h}\\U_{0}=4\pi *10^{-7}\\N=\frac{Bh}{U_{0}*I} \\N=\frac{0.25*0.6}{4\pi *10^{-7}*2.2}\\ N=54257 turns$

Sine it is circular, the length of the wire is

$L=N*2\pi r\\L=54257*2\pi *0.07\\L=23864\\L=23.9Km$