Magnetic sheilding from a Cylindrical Shell depending on the valule of mu, the sheilding capacity of a cylinder with a hollow inside half the value of the diameter of the cylider varies. Alpha (the field strengh at the center of the cylinder divided by the strength of the external field) can be calculated by counting the density of field lines inside the cavity and comparing it to the density of lines outside.

For mu=1.1 an outside field density of 5 lines per division was used. The sheilding was therefore calculated to be 1. There are the same number of lines inside the cavity as there would be without the sheild- it's hard to even see where the sheild is.

For mu=5, the outer feild line strength was increased to 10 lines per division, and the inner was measured to be 4, Alpha =.4

In both mu=10 and 20 12.5 lines per division were used, mu=10 has a sheilding of .32

and mu=20 is a sheilding of.2

In mu= 40 to 80, 33.3 lines per division were used for the outside feilds, ther are 4 lpd inside mu=40 has an alpha of .12

There is a sheilding of .06 for mu=60.

There are aprox, 1 2/3 lpd for mu=80, Alpha is therefore .05

mu=100 has 100 lpd, and Alpha was also calculated to be .05, it is time to take some larger steps.

For mu=200 to 400, there are 200 lines per division outisde, and no matter how small I make the step functoin, the internal lines were not evenly spaced. For mu=200 there are about 4 lpd, and alpha was calculated to be .02

For mu=300, there are about 2.5 lpd inside, Alpha is aprox, .013

For mu=400, there are about 4 lpd and Alpha is aprox, .01

For mu=500 there are 1,000 lines per(Outer) division, and 4 lpd internaly, Alpha is .004

For the rest of the graphs, there are 2,000 external lines per division, and dure to the unequal spacing of them, I took the averege spacing between them as the correct one For mu=600 there were 11 lpd, Alpha is .0055

For mu=700, there were 9 lpd, and alpha is .0045

For mu=800, there are 8 lpd, and alpha is .004

for mu=900, there are 6 lpd, and alpha is .003

Finaly, for mu=1,000 there are 5 lpd and alpha is .0025

Part 2, compartive pricing

In this problem we were to calculate how thick a sheild would be needed to reduce the magnetic feild strenght inside a hollow cylinder by .1 and how much it would cost with both mu=100 and mu=1000 matericals. To get a sheilding of .1 (I assumed you didn't mean increase the magnetic field lines in the cavity by a factor of 10) with a mu of 100 and a diameter increased to 10 cm, I sent in 10 field lines per division, when they dropped one line every div inside I would have the correct value

This happeded at a radius of 15 cm. There are 628 cm^3 per cm lengh. The cost per meter length of this material is (at $2.00 per kg and 7900 kg/m^3) $993

When mu was increased to 1000, this sheilding happeded at r=5.5cm The cost per meter length of this materical is $20.00 and there are 16.5 cm^3 per cm length. The cost per unit meter of this material is $261

I'd recomend going with the mu=1000 material, unless of course this is a project for the pentagon and you've already purchaced several $500 ashtrays.