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Maxwell's Equation Essay

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INTRODUCTION
Maxwell’s Equations are a set of four mathematical equations that provides the foundation to the largely abstract concepts of electricity and magnetism. They are a mathematical condensation of all the basic rules, by which electricity and magnetism function. Refer to Figure 1 for the equations.

Although James Clerk Maxwell himself only contributed to the last equation, his contribution led to one of the most important discoveries in the history of science. However, it wasn’t until 25 years later that these equations were interpreted and used rightly by the rest of the world. On the right is an image of Maxwell.
Maxwell’s work as quoted by Einstein:
‘The formulation of Maxwell's equations is the most important event in physics since Newton's time, not only because of their wealth of content, but also because they form a pattern for a new type of law …
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The equation is actually incomplete, and valid only for a long straight wire. An example to prove that it’s incomplete is given below.
Suppose a pot is taken and the exterior surface is considered the enclosed surface mentioned in the law, and the circumference of the bottom is considered to be the closed curve. When the equation uses the term ‘i’, it actually means the current enclosed within the path, piercing through the surface.
If the pot were shaped in such a way that the wire carrying current ended inside the pot after piercing through and coming out, current enclosed would be 0. This either means that dl and the magnetic field are always perpendicular (cosine 90 = 0), or that the magnetic field itself is 0. Both are impossible and there lies the contradiction.

MAXWELL’S CORRECTION

Maxwell corrected the equation by adding another term to it. Considering the above example, there is a change in electric field as the current pierces through one surface of the pot and goes out through the other. This field can be expresses
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