Foley et al.'s work suggests that humans may very well have this ability, and that the same proteins, called cryptchromes, which generate our circadian rhythm (our 24-hour biological clock) may allow us to sense magnetic fields:
Human Cryptochrome Exhibits Light-Dependent Magnetosensitivity, Nature Communications, May 2011
"Humans are not believed to have a magnetic sense, even though many animals use the Earth's magnetic field for orientation and navigation. One model of magnetosensing in animals proposes that geomagnetic fields are perceived by light-sensitive chemical reactions involving the flavoprotein cryptochrome (CRY). Here we show using a transgenic approach that human CRY2, which is heavily expressed in the retina, can function as a magnetosensor in the magnetoreception system of Drosophila and that it does so in a light-dependent manner.
The results show that human CRY2 has the molecular capability to function as a light-sensitive magnetosensor."
But the study doesn't address what our eyes or brains may be doing with this information:
"However, we do not yet know whether this capability is translated into a downstream biological response in the human retina.Wikipedia says that ESP or extrasensory perception "involves reception of information not gained through the recognized physical senses but sensed with the mind." I'm skeptical. However, sensing of magnetic fields, if we have the ability at all, would not fall under this heading since it looks to involve a physical sensor.
Nonetheless, the transgenic findings with hCRY2, together with its anatomical location in the human retina and previous work showing field effects on the visual system, suggest that a reassessment of human magnetosensivitiy may be in order."
I saw this study in a story on Science 2.0 this morning:
Protein In The Human Retina Can 'Sense' Magnetic Fields
The strength of a magnetic field "is proportional to the electrical current within the wire." The direction of the field depends on the direction of current. A magnetic field generated by a coil of wire has "a strength not only proportional to the current but also the number of loops in the coil."