Two narrow beams

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

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 2.0×107 m s−12.0\times10^{7}\,\text{m s}^{-1}. The region they enter contains a uniform magnetic field of 0.010 T0.010\,\text{T} 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∘90^{\circ} 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.

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