a volume. Solenoids and Helmholtz coils are types of coils that can be used for this purpose, as well as more complex wire patterns designed using methods adapted from those used in coil design for magnetic resonance imaging. Active shields may also be designed accounting for the electromagnetic coupling with passive shields, referred to as hybrid shielding, so that there is broadband shielding from the passive shield and additional cancellation of specific components using the active system. Additionally, superconducting materials can expel magnetic fields via the Meissner effect. Mathematical model Suppose that we have a spherical shell of a (linear and isotropic) diamagnetic material with relative permeability with inner radius and outer radius We then put this object in a constant magnetic field: Since there are no currents in this problem except for possible bound currents on the boundaries of the diamagnetic material, then we can define a magnetic scalar potential that satisfies Laplace's equation: where In this particular problem there is azimuthal symmetry so we can write down that the solution to Laplace's equation in spherical coordinates is: After matching the boundary conditions at the boundaries (where 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: where is an attenuation coefficient that depends on the thickness of the diamagnetic material and the magnetic permeability of the material: 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 . In the limit that this coefficient goes to 0 (perfect shielding). When , then the attenuation coefficient takes on the simpler form: which shows that the magnetic field decreases like See also Electromagnetic interference Electromagnetic radiation and health Radiation Ionising radiation protection Mu-metal MRI RF shielding Permalloy Electric field screening Faraday cage Anechoic chamber Plasma window References External links All about Mu Metal Permalloy material Mu Metal Shieldings Frequently asked questions (FAQ by MARCHANDISE, Germany) magnetic permeability Clemson Vehicular Electronics Laboratory: Shielding Effectiveness Calculator Shielding Issues for Medical Products (PDF) — ETS-Lindgren Paper Practical Electromagnetic Shielding Tutorial Simulation of Electromagnetic Shielding in the COMSOL Multiphysics Environment Magnetoencephalography Radio electronics Electromagnetic radiation Electromagnetic compatibility