# How any material can provide electrostatic and magnetic shielding

Several metallic objects like Iron, Copper etc can provide electrostatic shielding (one should remain inside the car during thunderstorm) and several superconductors like HTS (High Temperature Superconductors) provide magnetic shielding against the magnetic fields.

So how can such fields be repelled by these types of materials? I think it might be because of their atomic arrangement but I am still not sure that why only some of the elements from the periodic table (transition metals) provide these shielding. I mean every element in periodic table have some electrons, protons and neutrons. How these atomic arrangement influence them?

Also I want to know that why magnetic field is so specific in nature (it can be shielded only the zero resistance material). Is there any relation between the zero resistance material and it's magnetic shielding.

• This is pretty broad but I think there is an interesting question lurking in there somewhere. – Brandon Enright Nov 6 '14 at 16:32
• You might want to read the Wikipedia page on mu metal: en.wikipedia.org/wiki/Mu-metal – Jon Custer Nov 6 '14 at 20:26
• Ferroic(magnetic and polarization order parameters existing simultaenously and coupled) materials might be of interest. – John M Nov 10 '14 at 1:11

I think so. Electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. Electromagnetic radiation consists of coupled electric and magnetic fields. The electric field produces forces on the charge carriers (i.e., electrons) within the conductor. As soon as an electric field is applied to the surface of an ideal conductor, it induces a current that causes displacement of charge inside the conductor that cancels the applied field inside, at which point the current stops.

Mathematical model

Suppose that we have a spherical shell of a (linear and isotropic) diamagnetic material with permeability $\mu$, with inner radius a and outer radius b. We then put this object in a constant magnetic field:

$\vec{H}_{0}=H_{0}\hat{z}=H_{0}\cos\theta \hat{r}$

Since there are no currents in this problem except for possible bound currents on the boundaries of the diamagnetic material, i.e. $$\nabla\times \vec B=0$$ in a simply connected region, there exists a scalar function we call magnetic scalar potential such that $$\vec{H}=-\nabla \Phi_{M}$$ where $\vec{B}=:\mu \vec{H}$. Since $$\nabla\cdot\vec B=0$$ we have Laplace's equation: $$\nabla^{2}\Phi_{M}=0.$$

In this particular problem there is azimuthal symmetry so we can write down that the solution to Laplace's equation in spherical coordinates is:

$\Phi_{M}=\sum_{l=0}^\infty \left( A_{l}r^{l}+\frac{B_{l}}{r^{l+1}}\right)P_{l}(\cos\theta)$

After matching the boundary conditions \begin{align} (\vec{H_{2}}-\vec{H_{1}})\times \hat{n}&=0 \\ (\vec{B_{2}}-\vec{B_{1}})\cdot \hat{n}&=0 \end{align} at the boundaries (where $\hat{n}$ is a unit vector that is normal to the surface pointing from side 1 to side 2), then we find that the magnetic field inside the cavity in the spherical shell is:

$\vec{H_{in}}=\eta \vec{H_{0}}$

where $\eta$ is an attenuation coefficient that depends on the thickness of the diamagnetic material and the magnetic permeability of the material:

$\eta=\frac{9\mu}{(2\mu+1)(\mu+2)-2\left(\frac{a}{b}\right)^{3}(\mu-1)^2}$

This coefficient describes the effectiveness of this material in shielding the external magnetic field from the cavity that it surrounds. Notice that this coefficient appropriately goes to 1 (no shielding) in the limit that $\mu\rightarrow1$. In the limit that $\mu \rightarrow 0$, $\infty$ this coefficient goes to $0$ (perfect shielding), then the attenuation coefficient takes on the simpler form:

$\eta=\frac{9}{2} \frac{1}{(1-\frac{a^{3}}{b^{3}}) \mu}$

which shows that the magnetic field decreases like $\mu^{-1}$ Well I can tell u about electromagnetic shielding but not magnetic shielding. Sorry for that.

• $\LaTeX$ is denoted by enclosing in $ (for inline equations) or $$ (for displayed equations), not by spaces before the equations. E.g.$x^y$should be typed as $x^y\$. – Ruslan Nov 12 '14 at 16:44
• I just realized this answer is lifted verbatim from Wikipedia en.wikipedia.org/wiki/… without attribution. I added some steps of derivation before the realization. This is plagiarism. – Hans Feb 7 '18 at 20:36
• @Hans is it possible that wikipedia has copied this answer, perhaps unlikely, but given that it was from 3 years ago,.... and if not do we have a policy for this... I'm not sure. I'm not the one to ask - you could ask a meta question about this - BTW many thanks for your work making this site better by editing – tom Feb 7 '18 at 20:54
• @tom: Judging from the wikipedia version control history, that mathematical model section in the wikipedia article was in existence, in essentially the same form as the current version, in 2011. All that is needed is a reference. I just want to point this out and downvote. – Hans Feb 7 '18 at 21:07
• @Hans ok, sad that it was just lifted from Wikipedia... – tom Feb 7 '18 at 21:34

• Electrostatic Shielding - this is provided by metals which have 'free electrons'. In the metal some of the electrons from the atom can move about throughout the metal. These electrons provide the electrostatic shielding and this is also why metals appear to be 'shiny' they reflect light well because of the free electrons.

• Magnetic Shielding - Two cases

1) Superconductors - this is a special case because superconductors have no resistance they will prevent magnetic field lines passing through them - they make an electric current circulate inside them to exactly counteract and reduce to zero the magnetic field that approaches them.

2) Transition metals - ferromagnetic materials - Ferromagnetic materials have 'unpaired electrons'. These unpaired electrons generate magnetic fields, which can line up with or against magnetic fields. Special ferromagnetic materials can block magnetic fields - e.g. mu metal as mentioned in the Comment of Jon Custer above. Transition metals are unusual compared to other metals because they often have unpaired electrons. This is because of their position in the periodic table and the 'd' subshells.

You need to distinguish between "practical" shielding and "completely" shielding.

In the electrostatic case, any conductor (even a bad one) should adjust the charge distribution on its surface to reject the electric field - as long as an electric field exists the charge continues to experience a net force and will move. Note that lightning (for example) is NOT an electrostatic phenomenon and that the currents that flow during a lightning strike are definitely dynamic in nature. That said, the path that lightning will follow is, at least initially, in large part determined by the electric field distribution that exists before the strike - but the moment breakdown occurs (initiation of the lightning bolt) the field distribution changes. Still - you are better off inside the car than outside.

As for magnetics - the usual way to shield against magnetic fields is with mu-metal: this is a material with both high permeability, and therefore low reluctance: this means that when magnetic field lines exist in the vicinity of such material, they tend to be "attracted" towards it. This reduces the density of field lines inside - "shielding". See diagram (from http://optineer.com/Images/Mu%20Metal.jpg):

The property of the atoms that allows this kind of shielding, ultimately, is the electron configuration that permits an energetically beneficial coupling between adjacent atoms (ferromagnetism) - in other words, in the presence of a magnetic field the electron orbitals like to align with each other and this response causes magnetization of the material. This is strongest when the 3d orbital is unfilled - lots of helpful information at http://magician.ucsd.edu/essentials/webbookse18.html

Superconductivity is a different phenomenon: in this, the macroscopic flow of current (rather than the alignment of orbitals) is responsible for "rejecting" magnetic fields and thus providing shielding. This is just a limiting case of Lenz's Law which says that a circuit's current will change in response to a change in magnetic flux: in this case, the current will change until the flux is "back to zero". Note that if you make a loop superconducting when a B field already exists, it will maintain this magnetic field (because it rejects the change)...

The electrostatic shielding is not a matter of taking different materials. Its a matter of certain conditions which satisfy the potential difference to zero. so that no current flows through.

Take the case of a spherical metal.(eg :car )

Potential difference is given by (Electric field) times (the distance vector).

Since there is no charge inside a car, the electric field around any distance vector inside the car is zero. (By gauss law ).

Then the potential difference between any two points inside a car is zero. Therefore no charge flows.

Faraday Cage is a good example.