Magnetic force field particle trajectory

Since the magnetic force is always perpendicular to the direction of motion of the particle, it does not change the energy but only the direction of motion of the particle. If the velocity is perpendicular to the magnetic field, the particle trajectory will form a circle of radius p given by the equation... 

A charged particle (ze) moving in a uniform magnetic field will tend to follow a circular trajectory in which the (inward) magnetic force (zevB) is balanced by the (outward) centrifugal force (mv jr). ... 

Next, Fig. 5 shows a typical center of mass trajectory for the case of a full chaotic internal phase space. The eyecatching new feature is that the motion is no more restricted to some bounded volume of phase space. The trajectory of the CM motion of the hydrogen atom in the plane perpendicular to the magnetic field now closely resembles the random motion of a Brownian particle. In fact, the underlying equation of motion at Eq. (35) for the CM motion is a Langevin-type equation without friction. The corresponding stochastic Lan-gevin force is replaced by our intrinsic chaotic force — e B x r). A main characteristic of random Brownian motion is the diffusion law, i.e. the linear dependence of the travelled mean-square distance on time. We have plotted in Fig. 6 for our case of a chaotic force for 500 CM trajectories the mean-square distance as a function of time. Within statistical accuracy the plot shows a linear dependence. The mean square distance

of the CM after time t, therefore, obeys the diffusion equation... 

As a result of its passage through the applied magnetic field, the positively charged particle takes a circular trajectory of radius r. Intensity of the magnetic field being H, the force on the particle due to this magnetic field is Hev, which... 

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