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

23.9Km

Step-by-step 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=(U_(0)NI)/(h)\\U_(0)=4\pi *10^(-7)\\N=(Bh)/(U_(0)*I) \\N=(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`