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

TL;DR

This paper derives formulas for spherical volume averages of static electric and magnetic fields directly from Coulomb and Biot-Savart laws, avoiding vector calculus identities or potentials.

Contribution

It provides a novel derivation method for field averages that simplifies the process by not using vector calculus identities or potentials.

Findings

Derived explicit formulas for spherical volume averages of electric and magnetic fields.

Showed the derivations are nearly identical for both fields.

Eliminated the need for vector calculus identities in the derivations.

Abstract

We present derivations of the expressions for the spherical volume averages of static electric and magnetic fields that are virtually identical. These derivations utilize the Coulomb and Biot-Savart laws, and make no use of vector calculus identities or potentials.