page_title: Introduction to electromagnetism
section_title: Magnetic field
hierarchical_section_title: Introduction to electromagnetism / Magnetic field and force / Magnetic field
caption_attribution_description: English: The magnetic field of a bar magnet revealed by iron filings on paper. A sheet of paper is laid on top of a bar magnet and iron filings are sprinkled on it. The needle shaped filings align with their long axis parallel to the magnetic field. They clump together in long strings, showing the direction of the magnetic field lines at each point.Magyar: Rúdmágnes mágneses terének megjelenítése papírra szórt vasreszelékkel. A rúdmágnes tetejére egy papírlapot helyeztek, amelyre vasreszeléket szórtak. A tűalakú reszelékdarabkák tengelye a helyi mágneses térerősségvektorral párhuzamosan helyezkedik el. Hosszú fonalakká kapcsolódnak össze, így mutatva a mágneses erővonalak irányát minden egyes pontban. Español: El campo magnético de un imán se manifiesta por la distribución de las limaduras de hierro alrededor de dicho imán. Una hoja de papel reposa sobre un imán y las limaduras de hierro son esparcidas sobre el papel. Las limaduras de hierro se alinean con el campo magnético, de forma que muestran la dirección de las lineas de campo magnético en cada punto.
context_page_description: Electromagnetism is one of the fundamental forces of nature. Early on, electricity and magnetism were studied separately and regarded as separate phenomena. Hans Christian Ørsted discovered that the two were related – electric currents give rise to magnetism. Michael Faraday discovered the converse, that magnetism could induce electric currents, and James Clerk Maxwell put the whole thing together in a unified theory of electromagnetism. Maxwell's equations further indicated that electromagnetic waves existed, and the experiments of Heinrich Hertz confirmed this, making radio possible. Maxwell also postulated, correctly, that light was a form of electromagnetic wave, thus making all of optics a branch of electromagnetism. Radio waves differ from light only in that the wavelength of the former is much longer than the latter. Albert Einstein showed that the magnetic field arises through the relativistic motion of the electric field and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a quantum field in quantum electrodynamics.
context_section_description: The magnetic field is that which arises from moving charges, currents, and magnetic objects. The field is represented mathematically as a vector-valued function . The SI unit of the magnetic field is the tesla (T).
  The magnetic field can be derived mathematically using Ampère's law, the Biot–Savart law, or Maxwell's equations.
  Magnetic field lines have a very similar representation to electric field lines. There is an analogous notion of magnetic flux. Magnetic field lines begin at north poles and end at south poles, and cannot cross. Magnetic fields arise due to the motion of charges, and also due to the alignment of the domains of magnetic materials where the magnetic moments of the atoms point in the same direction.
  The modern (post-Einstein) interpretation is that the magnetic field is equivalent to the electric field, but in a different reference frame. Since magnetic fields can be interpreted as electric fields in a different reference frame (and vice versa), special relativity connects the two fields. One postulate of special relativity is length contraction, and because of that, the charge density in the wire increases, so a current-carrying wire viewed in a moving reference frame experiences a length-contracted coulomb force as compared to the wire in a stationary frame. This force is called the magnetic force, and the associated field is the magnetic field.  The direction of the magnetic force can be derived from the right-hand rule such that the force is perpendicular to both the direction of motion of the current (or charged particle) and the magnetic field.
caption: Magnetic field lines can be clearly visualized by sprinkling iron filings over a bar magnet.
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