The Math of Magnetic Shields

How Magnetic Shields Work

Magnetic shielding materials re-direct a magnetic field so it lessens the field's influence on the item being shielded. Shielding does not eliminate or destroy magnetic fields, nothing does. It does, however, provide an easy path for the magnetic field to complete its path. You may think of it as a magnetic field conductor.

This leads to what type of material can provide the best path for magnetic fields and thus create shielding. Since the field is attracted to the shielding material it stands to reason that if a magnet is attracted to the material (ferromagnetic material), that material can provide some amount of magnetic shielding.

Shield calculation formulas do exist to help solve electro magnetic shielding problems, but are usually valid only for theoretical conditions of closed shield shapes and well-described interference fields. Remember, one test is worth a thousand expert opinions. The easiest way to calculate magnetic shield values and properties is with our free-for-the-asking CO-NETIC® Magnetic Shield Calculator. This easy to use slide chart performs the calculations demonstrated below simply and quickly.

Formulas for magnetic calculations are based upon a perfect spherical shield and a point field source. These conditions are seldom encountered in practical shielding situations. However, the formulas can be helpful if modified for simplicity and used with discretion.

Also, technical data concerning the magnetic properties of shielding materials is based upon standard samples. Some variance in production runs may occur due to material thickness, annealing time and temperature tolerances.

We know that our shield will be dependent on the strength of the magnetic field it is in and how much of that field it occupies (the shield's physical size). We also know that the shield conducts or re-directs the magnetic field through the material from which the shield is made. Hence, the more material in the shield the more magnetic field it can re-direct. Putting all of this together we get a starting point for designing a shield.
B= (1.25*D*Ho) / t

Where:
» B = flux density in the shield material in gauss
» D = Diameter or diagonal of the shield in inches
» Ho = Ambient or source field in gauss
» t = Thickness of the shield in inches

B (flux density in the shielding material in Gauss) is the strength of the magnetic field that needs to be re-directed within the shield itself. It is important because once we estimate it we are able to see whether the shield can handle that much field. We do this by referring to the B-H (Flux Density - Magnetizing Force) curve for the shielding material. In our example we will use the curves for Magnetic Shield's Co-Netic and Netic materials.

Refer to Flux Density (B) vs. Permeability (µ) curve to obtain the permeability of the material when exposed to an ambient field that resulted in the B flux density obtained in Step 1. Find B on the left axis and scan across the graph to intersect the material curve. Find µ in the diagonal scales.

Approximate or expected attenuation can be determined by:
A = (µ * t) / D

Here is an example of using shielding equations to determine the attenuation obtained for a given material thickness:

Given a 2" diameter shield in a 2 gauss ambient field:
B= (1.25*2*2) / t = 5/t
When t = .014, then B = 367 gauss.

From the flux density vs. permeability curve, when B = 357, the permeability of the shield material would be approximately 140,000 gauss.
Then = A = (µ * t) / 0 = (140,000 * .014") / 2" = 980

Magnetic Shield has provided a simpler way to do these calculations but before we get to that there needs to be a little more discussion. Keep in mind that the calculations can provide a first step in designing a shield but they are not exact and should not be construed as a Law of Nature. Neither are the properties of the shielding materials going to be exact from one batch to the next. Nothing will take the place of using these formulas to make a prototype and testing the prototype under real world conditions.

Now that we've had a brief discussion of magnetic fields and shielding let's put the above information to work to design a prototype shield. Rather than going through all of the steps above, we'll use Magnetic Shield's Calculator to simplify the process. All you need to do is input D, the diameter or diagonal in inches that describes the size of the shield and HO, the strength of the field in Gauss where the shield will be located. Magnetic Shield's Calculator will do the rest and give you an estimate of the strength of the shielded field for each standard thickness of our Co-Netic AA Perfection annealed foil and sheet.

There are some restrictions. We have limited "D" to a range of ¼" to 12". If you go outside of this range you will be advised that "D" is either too large or too small. If you get the message that the field is too high it means you have entered into the "knee" of the B-H curve and will need a thicker material. Don't hesitate to contact us if you have a shield that doesn't fit the above criteria. Larger shields and higher magnetic fields are common.

Many electro magnetic shielding problems are solved by prototyping a magnetic shield from the materials in our Magnetic Shielding Lab Kit. The hands-on approach offers the advantages of being able to immediately see the results of the shielding in the item under test, and the opportunity to optimize the shield's thickness and shape.

How do I calculate ...

How do I determine attenuation ratios?

As an aid to determining this important value, we have developed an automated calculator. Simply input the Shield Diameter and measured Gauss values; then click on the calculate button. The online calculator will return the Attenuation Ratio value for your shielding project.

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