This is possible, it's just very very difficult to do.
People regularly do this with the electric field of light to move dielectric particles (insulators) in the lab, and the technique is known as "optical tweezers":
http://en.wikipedia.org/wiki/Optical_tweezers
The reason you don't want to try this with magnetic particles is that the magnetic field of light is much weaker than the electric field, or rather that it doesn't interact very much with most magnetic materials.
Greg's answer above is half correct - The fact that these fields oscillate in time means that the applied force would oscillate as well, however, the field gradient is exploited instead to make optical tweezers work.
Virtual photon clouds are responsible for potentials, not electric and magnetic fields, and this is what makes the explanation of forces in terms of photon exchange somewhat difficult for a newcomer. The photon propagation is not gauge invariant, and the Feynman gauge is the usual one for getting the forces to come out from particle exchange. In another useful gauge, Dirac's, the photons are physical, and the electrostatic force is instantaneous.
When you have a solenoid, the photons are generated by the currents in the solenoid, and a charge moving through this virtual photon cloud has an altered energy and canonical momentum according to the distribution of the photons at any point in space. The effect can be understood from the current-current form of the interaction:
$$ J^\mu(x) J^\nu(y) G_{\mu\nu}(x-y)$$
Where G is the propagation function, and the current J is the probability amplitude for emitting/absorbing a photon. The propagation function reproduces the vector potential from a source J, as it acts on another source J at another point.
There is no difference between classical sources producing photons and classical currents producing a vector potential--- they are the same. The electric and magnetic field description is not fundamental, and the gauge dependence of the photon propagator is just something you have to live with.
Best Answer
The human body produces a wide range of bioelectromagnetic signals from various electrical impulses in the brain. The origin of the magnetic field is the charge exchange in the muscular and neural tissues (i.e no magnetic material is usually present in the body with very rare exceptions).
The brain's magnetic field varies from 10s of fT to 100s of fT [1]. The frequency varies from 0.1 Hz to <100 Hz. Measurement of brain magnetism is limited by the complexity of signal due to the overlap of the signals from various parts of the brain. In magentoencephelograpahy this is done using SQUIDS [2].
The second part of your question is about magnetic excitement of brain functions. This is in fact possible and some testing/use is reported with limited clinical success. The strength of the applied magnetic fields are 1-5T for trans-cranial excitation [3].
[1] http://www.bem.fi/book/12/12.htm#02 [2] http://www.scholarpedia.org/article/Magnetoencephalogram [3] http://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation [4] http://www.bem.fi/book/22/22.htm An excellent source for this topic is [1]