Paper 1, Section I, C
(i) A particle of mass and charge , at position , moves in an electromagnetic field with scalar potential and vector potential . Verify that the Lagrangian
gives the correct equations of motion.
[Note that and .]
(ii) Consider the case of a constant uniform magnetic field, with , given by , , where are Cartesian coordinates and is a constant. Find the motion of the particle, and describe it carefully.
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