Assume that an electron is describing a circular orbit of radius a about a positively charged nucleus. (a) By selecting an appropriate current and area, show that the equivalent orbital dipole moment is ea2ω/2, where ω is the electron’s angular velocity. (b) Show that the torque produced by a magnetic field parallel to the plane of the orbit is ea2ωB/2. (c) By equating the Coulomb and centrifugal forces, show that ω is (4π0mea3 /e2) −1/2, where me is the electron mass. (d) Find values for the angular velocity, torque, and the orbital magnetic moment for a hydrogen atom, where a is about 6 × 10−11 m; let B = 0.5 T ?
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