Derivation of Maxwell-Faraday Equation

Michael Faraday is regarded as a great experimentalist. He noticed that a coiled wire created a field (when a current passed through it) that would cause another coiled wire (not in physical contact) to have an electric current measured by a current meter. The current flow in the first coil (when the current was changing) induced another current in the second coil. James Clerk Maxwell is known for the four equations of electromagnetism and derived the following formula based on Faraday’s induction experiment. See Feynman (1964):

?xE= - ∂B/∂t

Maxwell realized there is a field created by the changing current in the first coil. This is the phenomenon known as electromagnetic induction. Here in this paper the author will go through the mathematical steps Maxwell went through to come up with this formula. Maxwell used Stokes theorem which is. Feynman (1964):

? Γ E · ds = ∫s (?xE) · n da = - ∫s ∂B/∂t · n da

Γ is any closed curve and S is any surface bound by it. Γ is a mathematical curve fixed in space, and S is a fixed surface. Examining this gives the former formula. The author notes that the four Maxwell equations describe light as an electromagnetic procession of waves.