Ampère’s Equation and Maxwell’s Alteration

James Clerk Maxwell took André-Marie Ampère’s equation, which was for static charge, and added to it to include motion. Here in this paper the author will simplify the derivations to present a clear rendition of the mathematics. Both involve some calculation. Ampère’s equation is: (1)

ΦB ⋅ d l = μ0 I.

Maxwell added a term for motion, which resulted in this formula: (1)

ΦB ⋅ d l = μ0E0 ∫ ∂E/∂t ⋅ dS + μ0 I.

Where μ0 = permeability constant and E0 = permittivity constant. Now c, the speed of light, = 1 / (μ0E0)1/2. [2] Here the author will outline the calculations for Ampère’s and Maxwell’s equations. (2), (3), (4).