# Why doesn't ordinary metal box shield magnetic field?

I have this metal box. I put a transformer inside.

Using a magnetic field meter. I can still measure 80 milligauss out of the original 100 milligauss.

Why didn't it complete block it? What would it take to complete block it?

• It depends on what the metal box is made of. Different metals have different magnetic properties. – BioPhysicist Oct 29 '18 at 22:41
• Why do you expect that a metal box blocks this magnetic field? – my2cts Oct 29 '18 at 22:41
• because the metal box can produce current out of the magnetic field so can reduce or remove it.. but why 75% or so still retained? – Samzun Oct 29 '18 at 22:56
• For ac magnetic fields, yes, there should be some reduction in the intensity of the magnetic fields since eddy currents generated in the metal shield should act against changing magnetic fields. But it won't be complete cancellation. Also, a high permeability mu-metal shield may work for 60 Hz fields. I dunno. You may want to take this problem over to the folks over at electrical engineering stack exchange. – user93237 Oct 29 '18 at 23:10
• This is a physics problem because it involves understanding the physics of fluxes which electrical engineers are not expert of. I want to understand why there is no complete cancellation.. and why you need mu-metal shield for that? – Samzun Oct 29 '18 at 23:13

Assuming you're measuring the amplitude of magnetic field oscillations:

Radiation penetrates through a conductor to a depth on the order of the quantity known as the skin depth $$\delta$$, which, for good conductors and low frequencies, is given by

$$\delta = \sqrt{\frac{2\rho}{\omega \mu}}$$

for a conductor with resistivity $$\rho$$ and magnetic permeability $$\mu$$ and radiation at frequency $$\omega$$. For aluminum, $$\rho=2.65\times 10^{-8}\;\Omega\text{m}$$ and $$\mu=1.26\times 10^{-6}\;\text{H/m}$$, so $$\delta\approx 3\;\text{cm}$$. For steel, $$\rho\approx 5\times10^{-7}\;\Omega\text{m}$$ and $$\mu$$ ranges from $$10^{-6}$$ to $$10^{-3}$$ $$\text{H/m}$$, so $$\delta$$ ranges from $$4\;\text{mm}$$ to $$12\;\text{cm}$$, depending on the type of steel. In any case, it should be clear that it may take several centimeters of conductive shielding to insulate 60-Hz radiation, and it doesn't appear that the metal box is quite that thick. Low-frequency radiation is penetrating by nature, and therefore hard to insulate.

Assuming you're measuring the DC (steady) magnetic field:

First of all, the Earth's magnetic field is 250-650 milligauss, which is on the order of both of your measurements, so if you haven't zeroed your measurement properly or otherwise haven't replicated experimental conditions properly, you might just be measuring a local variation of the Earth's magnetic field, or the metal box's distortion of that field independent of the field of the transformer. In any case, though, you can't really "block" or "absorb" DC magnetic fields, you can only divert them, which is done through materials with high permeability. The permeability of metals varies widely (over three orders of magnitude for steel alone), and it's incorrect to assume that most metals are good at insulating DC magnetic fields. One of the more common high-permeability metals around is called Mu-Metal, with a permeability of around $$10^{-2}\;\text{H/m}$$, which is 10,000 times greater than that of aluminum and 10 times greater than high-permeability steel.

• I'm measuring 60 Hertz ac field. So only Mu-Metal can block it? Do you also say that Mu-Metal can also block DC magnetic fields. This means Mu-Metal box can block both AC and DC fields? Are there commercially available Mu-metal box I can buy and experiment? – Samzun Oct 30 '18 at 0:05
• @Samzun In either case, you can improve your situation by either making the box thicker or making it out of a different metal. For the AC field insulation, both the resistivity and the permeability of the metal matter; for the DC field insulation, permeability is the dominant factor. So in the DC case, it's clear that Mu-metal would be superior. As it happens, Mu-metal also has a resistivity comparable to steel, so even a thin box of Mu-metal would work in the AC case (skin depth is only 0.6 mm by the formula above). Mu-metal is commercially available, though you may have to get a quote. – probably_someone Oct 30 '18 at 0:13