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A particle of charge e and mass m moves in a region of uniform electric field E directed along Ox and a uniform magnetic field B directed along Oz. Show that one solution (called a particular integral) is x=0, y=-Et/B,z=0, and that the general solution of the motion in the xy-plane is x= R sinw(t-t0)+x0 y= R cosw(t-t0)+y0-Et/B where w=eB/m is the cyclotron frequency. Thus the particle executes circles superposed upon a drift velocity E/B perpendicular to both E and B. The radius R and other constants are determined by the initial conditions.

By using the Lorentz force, i get enter image description here

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  • $\begingroup$ I would suggest starting from the Lorentz force, constructing some general position and velocity vectors to work with in this Lorentz force expression $\endgroup$ – Jordan Simba Jul 22 '18 at 20:45
  • $\begingroup$ Consider taking the time derivative of the second order differential equation in y and equating the x derivative terms. $\endgroup$ – Jordan Simba Jul 22 '18 at 21:57

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