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Register a new userEquivalence of total force (and torque) for two formulations of the Lorentz law
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Two formulations of the Lorentz law of force in classical electrodynamics yield identical results for the total force (and total torque) of radiation on a solid object. The object may be surrounded by the free space or immersed in a transparent dielectric medium such as a liquid. We discuss the relation between these two formulations and extend the proof of their equivalence to the case of solid objects immersed in a transparent medium.
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It is shown that the mathematical form, obtained in a recent paper, for the angular momentum of the electromagnetic field in the vicinity of electric charge is equivalent to another form obtained previously by Cohen-Tannoudji, Dupont-Roc and Gilbert. In this version of the paper an improved derivation is given.
Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of SDO/HMI vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging ARs size, the emergence rate, or the non-potentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.
We present concise, computationally efficient formulas for several quantities of interest -- including absorbed and scattered power, optical force (radiation pressure), and torque -- in scattering calculations performed using the boundary-element method (BEM) [also known as the method of moments (MOM)]. Our formulas compute the quantities of interest textit{directly} from the BEM surface currents with no need ever to compute the scattered electromagnetic fields. We derive our new formulas and demonstrate their effectiveness by computing power, force, and torque in a number of example geometries. Free, open-source software implementations of our formulas are available for download online.
Using the Finite-Difference-Time-Domain (FDTD) method, we compute the electromagnetic field distribution in and around dielectric media of various shapes and optical properties. With the aid of the constitutive relations, we proceed to compute the bound charge and bound current densities, then employ the Lorentz law of force to determine the distribution of force-density within the regions of interest. For a few simple cases where analytical solutions exist, these solutions are found to be in complete agreement with our numerical results. We also analyze the distribution of fields and forces in more complex systems, and discuss the relevance of our findings to experimental observations. In particular, we demonstrate the single-beam trapping of a dielectric micro-sphere immersed in a liquid under conditions that are typical of optical tweezers.
In several experiments involving material background, it has been observed that the Chu, Einstein-Laub and Ampere formulations of optical force lead to either different optical forces or wrong total optical force. In order to identify the exact reason behind such significant disagreements, we investigate the optical force in a number of tractor beam and lateral force experiments. We demonstrate that the modified Einstein-Laub or modified Chu formulations, obtained from two mathematical consistency conditions of force calculation, give the time-averaged force that agrees with the experiments. We consider both the chiral and achiral objects embedded in complex material backgrounds. Though the distinct formulations of optical force have been made mathematically equivalent in this work; the aspect of physical consistency of these distinct optical force formulations have also been investigated. It is known that the theory of Minkowski suggests zero bulk force inside a lossless object for which we still do not have any experimental verification. In contrast, both modified Einstein-Laub and modified Chu force formulations suggest non-zero bulk force inside a lossless object. Hence, for a future resolution of this discrepancy, we also suggest a possible experiment to investigate the bulk force and to check the validity of these distinct formulations.
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