Why doesn't ordinary metal box shield magnetic field?

Question

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?

Answer 1

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.