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One method of introducing electric field is based on the measurement of the force acting on moving charged particle. By equating F to qE we determine the electric field E if the electric charge q is known. Similarly, one can determine magnetic field.

This approach is fine for vacuum but it generally fails for fields in a medium, especially for dispersive medium since one needs first to distigush Lorentz force from other forces that act on a particle there, e.g., from friction force. Once I met the above cited description somewhere but I forgot where it was written. Could some one direct me to an approriate reference? I also cannot remember tha name of scientist who pointed out on the above cited difficulty in determining the field. Perhaps, it was Rosenfeld or something like that. And finally, is there a better definition of the electric / magnetic field in a medium?

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There are lot of phenomena where electric and magnetic fields can be measured. The simplest example: Stark and Zeeman effects. They work in medium absolutely like they work in vacuum for all particles involved with exception for the valence electrons in semiconductors and metals. For them they work also, but not "as in vacuum".

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