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Brain activity can be measured using magnetic fields located at some distancefrom the brain, a technique called magneto-encephalography (MEG). The origin ofsuch magnetic fields are the ionic currents involved in neuronal activity.While these processes are well known at the microscopic scale, it is less clearhow large populations of neurons generate magnetic fields. Here, we attempt tomake such a link by deriving a mean-field theory of magnetic field generationby populations of neurons. We use the concept of current dipoles to build atheory that can be applied to populations of neurons. We also evaluate thecontributions of neuronal current sources such as the synaptic currents oraction potential currents. This theory should be useful to calculate themagnetic field located at long distances from neuronal populations, such as inMEG.

A formalism for the long-distance magnetic field generated by populations of neurons