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According to particle physics , every fundamental force has its force carrier particle. Photon is a force carrier particle of electromagnetic force but

What is the process through which magnetic field applies attractive and replusive force through photons ?

  • Have a look at my answer here http://physics.stackexchange.com/questions/220018/how-can-photons-cause-charges-to-attract/220100#220100 for charges – anna v Dec 18 '15 at 18:11

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It is hard to explain intuitively. however repulsion is mediated -as you know- momentum throwing between electrons. however attraction must be though differently. if you sum over all virtual photons you end up some Feynman diagram that shows two electrons shooting a photon out so that they are shifted towards each other. the two outgoing photons are actually the same one.( understand it quantum mechanically). in this way - and + s attract and - and - s or + with +s repulse( a more deep explanation of this is the Pauli exclusion principle. therefore - electrons or + anti electrons try not to be in the same position.)