Magnetism · Part 2

large distances, and (ii) is subject to torque like a magnetic needle. This led Ampere to suggest that all magnetism is due to circulating currents. This seems to be partly true and no magnetic monopoles have been seen so far. However, elementary particles such as an electron or a proton also carry an intrinsic magnetic moment, not accounted by circulating currents. . . The magnetic dipole moment of a revolving electron In Chapter we shall read about the Bohr model of the hydrogen atom. You may perhaps have heard of this model which was proposed by the Danish physicist Niels Bohr in and was a stepping stone to a new kind of mechanics, namely, quantum mechanics. In the Bohr model, the electron (a negatively charged particle) revolves around a positively charged nucleus much as a planet revolves around the sun. The force in the former case is electrostatic (Coulomb force) while it is gravitational for the planet-Sun case. We show this Bohr picture of the electron in Fig. . . The electron of charge (– e) ( e = + . × – C) performs uniform circular motion around a stationary heavy nucleus of charge + Ze . This constitutes a current I , where, e I T ( . ) and T is the time period of revolution. Let r be the orbital radius of the electron, and v the orbital speed. Then,
r T = v ( . ) Substituting in Eq. ( . ), we have I = ev / π r . There will be a magnetic moment, usually denoted by µ l , associated with this circulating current. From Eq. ( . ) its magnitude is, µ l = I π r = evr / . The direction of this magnetic moment is into the plane of the paper in Fig. . . [This follows from the right-hand rule discussed earlier and the fact that the negatively charged electron is moving anti-clockwise, leading to a clockwise current.] Multiplying and dividing the right-hand side of the above expression by the electron mass m e , we have, ( l e e