Genghis,
Unfortunately, a Faraday cage only protects against the electro-magnetic fields and electrostatic fields, but not against magnetic fields. An intuitive explanation of the difference is that close to the radiating device, the separate electrostatic and magnetic fields dominate, while farther away (more than a wavelength or so) they 'combine' to produce what we call radio waves or electromagnetic radiation.
The braided, grounded shield found in most signal cables aboard aircraft protects against EM radiation, and electrostatic fields, but not magnetic fields.
Effective shielding against magnetic fields can be achieved by twisted-pair wiring/differential inputs (generally already implemented) coupled with ferrous (read:iron) shielding which is not generally implemented due to weight and cost reasons.