A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a specialized branch of mathematics, is normally inaccessible to the majority of engineers and engineering students. This paper provides for the first time a proof that greatly reduces the dependence on Differential Geometry (the reader only needs to be aware of the concept of "curvature"). The emerging applications of the theorem in computational field problems are also discussed here.