A particle with negative charge q and mass m = 2.58 X 10-15 kg is travelling through a region containing a uniform magnetic field B = - (0.120 T) k. At. a particular instant of time the velocity of the particle is v = (1.05 X 106 m/s)( -3i + 4j + 12k) and the force F on the particle has a magnitude of 1.25 N.
(a) Determine the charge q.
(b) Determine the acceleration Ii of the particle.
(c) Explain why the path of the particle is a helix, and determine the radius of curvature R of the circular component of the helical path.
(d) Determine the cyclotron frequency of the particle.
(e) Although helical motion i. not periodic in the full sense of the word, the x- and y-coordinates do vary in a periodic way. If the coordinates of the particle at t = 0 are (x, y, z) = (R, 0, 0), determine its coordinates at a time t = 2T, where T is the period of the motion in the xy-plane.