Consider a particle of mass m, charge q, and constant speed v moving perpendicular to a uniform magnetic field of magnitude B, as shown in Figure 31-42. The particle follows a circular path. Suppose the angular momentum of the particle about the center of its circular motion is quantized in the following way: mvr = nh, where n = 1, 2, 3, c, and h = h/2π.

a. Show that the radii of its allowed orbits have the following values:

b. Find the speed of the particle in each allowed orbit.

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nh п дв