We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by M...We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by Mansuripur to resolve a seeming paradox concerning the Lorentz force law and relativity. Our results provide new insights into electromagnetic theory, since they provide a unified and general treatment of the balance of lineal and angular momentum that permits a better assessment of some torques. Thus in this work we extend the derivations we have made of balance equations for electromagnetic linear momentum to balance equations for electromagnetic angular momentum. These balance equations are derived from the macroscopic Maxwell equations by means of vector and tensor identities and from the different ways in which these equations are written in terms of fields E, D, B, and H, as well as polarizations P, and M. Therefore these balance equations are as sound as the macroscopic Maxwell equations, with the limitations of the constitutive relations.展开更多
With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these ...With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.展开更多
We present a non-relativistic approach to the equivalent polarization Peq=(1/c2)v×Meq, that appears in a magnetized medium in motion. We apply an analogous method to that used by Panofsky and Phillips to calculat...We present a non-relativistic approach to the equivalent polarization Peq=(1/c2)v×Meq, that appears in a magnetized medium in motion. We apply an analogous method to that used by Panofsky and Phillips to calculate the symmetric effect, the equivalent magnetization that appears in a polarized dielectric in motion, Meq=P×v,?This method is based on a particular expression of Maxwell’s equations and the application of the convective derivative. These authors argue, however, that the equivalent polarization can be obtained only with a relativistic approach. We show that with the same method, but with a different and equivalent expression of Maxwell’s equations, this effect can also be calculated. In this way both effects can be considered relativistic effects to first order in v/c.展开更多
文摘We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by Mansuripur to resolve a seeming paradox concerning the Lorentz force law and relativity. Our results provide new insights into electromagnetic theory, since they provide a unified and general treatment of the balance of lineal and angular momentum that permits a better assessment of some torques. Thus in this work we extend the derivations we have made of balance equations for electromagnetic linear momentum to balance equations for electromagnetic angular momentum. These balance equations are derived from the macroscopic Maxwell equations by means of vector and tensor identities and from the different ways in which these equations are written in terms of fields E, D, B, and H, as well as polarizations P, and M. Therefore these balance equations are as sound as the macroscopic Maxwell equations, with the limitations of the constitutive relations.
文摘With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.
文摘We present a non-relativistic approach to the equivalent polarization Peq=(1/c2)v×Meq, that appears in a magnetized medium in motion. We apply an analogous method to that used by Panofsky and Phillips to calculate the symmetric effect, the equivalent magnetization that appears in a polarized dielectric in motion, Meq=P×v,?This method is based on a particular expression of Maxwell’s equations and the application of the convective derivative. These authors argue, however, that the equivalent polarization can be obtained only with a relativistic approach. We show that with the same method, but with a different and equivalent expression of Maxwell’s equations, this effect can also be calculated. In this way both effects can be considered relativistic effects to first order in v/c.
