The MEG or magneto-encephalogram does that. Uses an array of supercooled magnetic pickups to measure brain electrical activity not only at the surface, but at depth.
It is possible to detect biopotential signals without body contact. A paper by R J Prance et al (2000 Meas. Sci. Technol. 11 291-297, "An ultra-low-noise electrical-potential probe for human-body scanning") describes "a very-low-noise, high-input-impedance probe developed to make non-contact measurements of electrical potentials generated by currents flowing in the human body. With a noise level of 2 µV Hz-1/2 at 1 Hz, down to 0.1 µV Hz-1/2 at 1 kHz, and an operational bandwidth from 0.01 Hz to 100 KHz..."
I have provided links to the papers (and circuit diagrams) that are available online at: