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particle accelerators work by accelerating a charged particle in a magnetic field where the lines of magnetic flux are such that the particle is accelerated into a circular path. This is so that the force produced by such a motion and magnetic field is perpendicular to both the lines of magnetic flux and the velocity of the particle.

The stronger the magnetic field and the faster the particle is moving, the more of a force is required (i.e stronger magnetic field) to keep the particle accelerating.

Only a charged particle is affected by a magnetic field so only charged particles can be used inside a particle accelerators (i.e protons and electrons.) neutrons have a charge of zero and are not affected by magnetic fields.

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