There was a question several days ago related to visualizing the electro-magnetic field. I reminded me of a great passage from the Feynman Lectures on Physics. I won't quote the whole thing, but it is in section 20-3, "Scientific Imagination" (unfortunately I don't think the lectures are available on google books). I highly recommend this passage; it discusses more than just the electromagnetic field. A brief excerpt: Note his use of the word "unfortunately"! For my own part, these visualizations are also very vague for me, but I do think that with the advent of electromagnetic simulators it is perhaps a little easier for us today to get visualizations of the fields.