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I was looking at search terms that lead people to this website from Google and stumbled across this one: “the work done by the magnetic field on the charged particle during the semicircular trip.” Someone obviously was interested in how much work a magnetic field could “do”, and Google was kind enough to point them to this forum topic. Luckily my response way back in 2005 was accurate. I would like to expand on it here, though, since many students (actually, most of them) get this wrong, and many a crack-pot theory is based on an incorrect premise. The magnetic field does NO work on a charged particle. In fact, the only thing a magnet can do work on is another magnet or a ferromagnetic material.

Work has a specific definition in physics. It is the dot-product of the force and displacement vectors:

For two vectors, the dot-product is given by:

The force on a charge due to a magnetic field is given by the cross-product of the charge’s velocity vector and the magnetic field vector:

Short version: the force vector is perpendicular to both the velocity vector and the magnetic field vector. (BTW, many students miss this one, too: the charge must have a velocity and therefore must be moving for there to be a magnetic force.) The direction of the force is given by the right-hand rule we talk about at great length.

So, back to the definition for work:

The particle is moving in the direction of the velocity, so the displacement vector will be in the same direction. The magnetic force is always perpendicular to the velocity vector, therefore …

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The magnetic field can do no work on a charge.