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 electromagnetism vector fields 

By the time of Maxwell, physicists long realized that vector fields offered the perfect way to describe either electricity or magnetism. Take a bar magnet, place it on a flat sheet of paper, and sprinkle iron filings throughout the sheet. Amazingly, the filings will typically start to arrange themselves along distinct curves, branching out from the magnet’s poles. Trace each of those curves from the north pole of the magnet to the south pole, and those are the magnetic field lines. The strength of the field at each point matches the closeness of the field lines, and the direction matches their angles. Clearly, therefore, magnetism is well-represented by a vector field. Similarly, electricity near charged objects can be described by a vector field as well. 

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