Related papers: The vector potential of a steady azimuthal current…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonstrate that its more general expression is the vectorial product of the current density with the vector potential. We associate this Larmor's…
Motivated by the example of the superconducting cosmic string which can be a physical representation of a straight wire carrying a steady current, we derive in this case the explicit expressions of the induced vector potential, current…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The…
The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the…
Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's…
A forgotten experiment by Andr\'e Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced $emf$: the physical agent is instead…
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.
In Rindler space, we determine in terms of special functions the expression of the static, massive scalar or vector field generated by a point source. We find also an explicit integral expression of the induced electrostatic potential…
A method to derive the charge current density and its quantum mechanical correlation from the scattering matrix is discussed for quantum scattering systems described by a time-dependent Hamiltonian operator. The current density and charge…
We show that the time-dependent particle density $n(\vec r,t)$ and the current density ${\vec j}(\vec r,t)$ of a many-particle system that evolves under the action of external scalar and vector potentials $V(\vec r,t)$ and $\vec A(\vec…
We present an educational path on the magnetic vector potential A addressed to undergraduate students and to pre-service physics teachers. Starting from the generalized Ampere-Laplace law, in the framework of a slowly varying time-dependent…
The expression for the Coulomb-gauge vector potential in terms of the `instantaneous' magnetic field derived by Stewart [2003 Eur. J. Phys. 24, 519] by employing Jefimenko's equation for the magnetic field and Jackson's formula for the…
We derive an analytic solution for the electromagnetic vector potential in any gauge directly from Maxwell's equations for potentials for an arbitrary time-dependent charge-current distribution. No gauge condition is used in the derivation.…
We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and…
A circuit is considered in the shape of a ring, with a battery of negligible size and a wire of uniform resistance. A linear charge distribution along the wire maintains an electrostatic field and a steady current, which produces a constant…
Electric vector potential $\Theta(\boldsymbol{r})$ is a legitimate but rarely used tool to calculate the steady electric field in free-charge regions. Commonly, it is preferred to employ the scalar electric potential $\Phi(\boldsymbol{r})$…
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. That current includes, apart from the well-established delta-function term which is sufficient for its…