Abstract:
We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an “orbital” and “spin” nature. All three expressions are different, and there seems to be no reason to prefer one to another. It appears, on the basis of classical electrodynamics, that there is no unique way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in a fixed inertial frame. 1. Introduction The total angular momentum of the electromagnetic field is given (in SI units) [1] by Henceforth, we will suppress the time coordinate of the fields, all of which depend on time, and also the factor. There has been debate for a long time over whether the total angular moment of the electromagnetic field can be decomposed into an orbital part and a spin part so that Some authors [2] argue that on the basis of the first principles it is not possible to do this; others [3–5] show that forms can be demonstrated that appear to be, at least algebraically, of a spin and orbital nature. By means of partial integration Ohanian [4] effected a decomposition with , where is the vector potential and is the gradient operator that operates on functions of . Ohanian assumed that the electric charge density was zero and deemed (3) and (4) to be the spin and orbital components, respectively, of the electromagnetic field on the basis that the integrand of (3) was not explicitly linear in the coordinate whereas the integrand of (4) was. When the charge density is not zero, a bound term , considered also to be of an orbital nature is obtained on whose form all writers agree [6]. Although the sum of (3) and (4) and (5) is gauge invariant, the individual terms are not and so have no physical interpretation until the gauge of the vector potential is fixed completely. Cohen-Tannoudji et al. [3] used the Coulomb (or transverse) gauge, defined by the gauge condition , which gives The bound component remains the same as (8). It will be shown in Section 2 that the terms that involve the scalar potential in (6) and (7) cancel so that in (6), (7), and (8) and in (9), (10), and (8) but in (6) differs from in (9) and in (7) differs from in (10). The forms of (9) and (10) have also been used by van Enk and Nienhuis [5]. The general explicit form for , given in (13), was not specified by these writers. On the other hand, Stewart [7] found a decomposition from decomposing the electric field by the Helmholtz theorem [8]: This decomposition uses the and fields throughout so no issues of gauge arbitrariness arise.

Abstract:
exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of diferent dispersion rules are given in terms of the lambert w function. these dispersion rule dependent "wien peaks" are compared to those wavelengths obtained in a setting independent of the dispersion rule chosen where the "peak" wavelengths are taken to be those obtained on dividing the total radiation intensity emitted from a blackbody into a given percentile. the account provides a simple yet accessible example of the growing applicability of the lambert w function in physics.

Abstract:
the ready availability of very strong permanent magnets in the form of rare-earth magnetic alloys such as neodymium-iron-boron has lead to renewed interest in one of the oldest types of electric motors - the homopolar motor. the ease with which a demonstration homopolar motor can now be built and operated when neodymium magnets are used is quite remarkable. in this paper some simple homopolar motors employing neodymium magnets suitable for demonstrational purposes are described and discussed.

Abstract:
Dear Editor:This letter addresses the following sentence in the "Mobility redux: Post-World War II prosthetics and functional aids for veterans, 1945 to 2010" editorial that appeared in JRRD, Volume 48, Number 2. The sentence on page xv, second column: "Early testing and rigorous subject feedback clearly showed that DEKA II's first active socket design was not what patients wanted or needed." is not accurate. There is evidence in the historical literature on problematic prosthetic sockets. However, user response to the interface design introduced as part of the DEKA Arm System in collaboration with prosthetists at biodesigns, Inc (Santa Monica, California) and Next Step Orthotics and Prosthetics, Inc (Manchester, New Hampshire) has been quite favorable.It would be accurate to say "Early testing and rigorous subject feedback clearly showed that the active socket design used as part of the DEKA Arm System offers significant benefits and was positively received by research subjects."

Abstract:
In view of the recent work by Karkantzakos [Journal of Engineering Science and Technology Review 2 (2009) 76–81], anumber of remarks highlighting the connection between the Lambert W function and the time of flight and range of a projectilemoving in a resisting medium where the retarding force acting on the projectile is proportional to its velocity are made.In particular, we show how each of these quantities can be expressed in closed form in terms of the Lambert W function andindicate how the analysis of the motion becomes greatly simplified by its introduction.

Abstract:
The angular momentum of the physical electron, modelled as a Dirac fermion coupled to the electromagnetic field, is found to be hbar/2, the same as that of a bare Dirac fermion and independent of the size of the electric charge.

Abstract:
A proof is given of the vector identity proposed by Gubarev, Stodolsky and Zakarov that relates the volume integral of the square of a 3-vector field to non-local integrals of the curl and divergence of the field. The identity is applied to the case of the magnetic vector potential and magnetic field of a rotating charged shell. The latter provides a straightforward exercise in the use of the addition theorem of spherical harmonics.

Abstract:
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.