(Motion of a charged mass) Consider a particle of mass m, carrying an electrical charge q,and moving in a uniform magnetic field of strength B. The field is in the positive z direction. The equations of motion of the particle are
Mx″ = qBy′,
my″ = −qBx′, (9.1)
mz″ = 0,
where x(t),y(t),z(t) are the x,y,z displacements as a function of the time t.
Show that by a suitable choice of initial conditions the motion can be a circle in the x,y plane, of any desired radius R and centered at any desired point x0, y0. Propose such a set of initial conditions.
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