Two narrow beams, one of protons and the other of electrons, are launched simultaneously from the same point toward the east with identical speeds of 2.0×107m s−1. The region they enter contains a uniform magnetic field of 0.010T directed vertically into the plane of the page.
(i) Show that each beam follows a circular trajectory and obtain the radius of the path for the protons and for the electrons separately.
(ii) After each particle has moved through exactly 90∘ of its respective circle, calculate the straight-line distance between the proton and the electron.
(iii) Draw a neat, labelled sketch indicating the initial directions of the magnetic forces on both particles and the sense of their subsequent motion.