Spherical volume averages of static electric and magnetic fields using Coulomb and Biot-Savart laws

Biot-Savart-like law in electrostatics

The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by deriving a Biot-Savart-like law suitable for calculating electric fields. We show that, under certain circumstances, the traditional Dirichlet problem can be mapped onto a much simpler Biot-Savart-like problem. We find an integral expression for the electric field due to an arbitrarily shaped, planar region kept at a fixed electric potential, in an otherwis…

Experimental Evidence on Non-Applicability of the Standard Retardation Condition to Bound Magnetic Fields and on New Generalized Biot-Savart Law

In this work we made an analysis of the current status of velocity dependent (bound) field components in the framework of the standard electromagnetic theory. Preliminary discussions of the structure of the magnetic field due to an idealized oscillating magnetic dipole provided us with the quantitative insights on the relative contribution of velocity dependent (bound) and acceleration dependent (radiation) terms into the resultant magnetic field. According to this analysis we defined the methodological scheme based on a generalized (time-dependent) Biot-Savart law capable to test the applicab…

Comment on `About the magnetic field of a finite wire'

A flaw is pointed out in the justification given by Charitat and Graner [2003 Eur. J. Phys. vol. 24, 267] for the use of the Biot--Savart law in the calculation of the magnetic field due to a straight current-carrying wire of finite length.

Electrostatic Field of Angular-Dependent Surface Electrodes

We present an analytic strategy to find the electric field generated by surface electrode SE with angular dependent potential. This system is a planar region $\mathcal{A}$ kept at a fixed but non-uniform electric potential $V(ϕ)$ with an arbitrary angular dependence. We show that the generated electric field is due to the contribution of two fields: one that depends on the circulation on the contour of the planar region ---in a Biot-Savart-Like (BSL) term---, and another one that accounts for the angular variations of the potential in $\mathcal{A}$. This approach can be used to find exact solu…

How a charge conserving alternative to Maxwells displacement current entails a Darwin like approximation to the solutions of Maxwells equations

Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector potentials are expressed in terms of the charge and current densities. The magnetic field is shown to satisfy the Biot_Savart Law. The electric field is shown to be the sum of the gradient of a scalar potential and the time derivative of a vector potential which is different from but just as tractable as the simplest vector potential that yields the Biot_Savart Law T…

为什么关于位移电流的争议从未结束？

Why the controversy over displacement currents never ends?

本文借助亥姆霍兹分解澄清了位移电流是否产生磁场的百年争议，指出非稳恒电流下磁场无法定义且其效应已自动包含在毕奥-萨伐尔定律的计算中。