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## James Clerk Maxwell’s statue

In May I was in Edinburgh to compete in the Edinburgh marathon. On the day after the marathon I did a sight-seeing tour of Edinburgh. One of the things I saw was a statue to the Scottish mathematical physicist James Clerk Maxwell. The statue is at the Saint Andrew Square end of George Street, abut 300 metres from the famous Princes Street.

James Clerk Maxwell was an important physicist and mathematician. His most prominent achievement was to formulate the equations of classical electromagnetic theory. These four equations are known as Maxwell’s equations. They are shown on a small plaque at the rear of the statue’s plinth. The rear of the statue’s plinth. The larger plaque is illustrated in the bottom photograph. Below this is a small plaque with Maxwell’s four famous equations of electromagnetism. $\boxed{ \begin{array}{lcll} \nabla \cdot \vec{D} & = & \rho & (1) \\ & & & \\ \nabla \cdot \vec{B} & = & 0 & (2) \\ & & & \\ \nabla \times \vec{E} & = & - \frac{\partial \vec{B}}{\partial t} & (3) \\ & & & \\ \nabla \times \vec{H} & = & - \frac{\partial \vec{D}}{\partial t} + \vec{J} & (4) \end{array} }$

These equations are written in differential form, where the symbol $\nabla$ is known as the vector differential operator. I will explain the mathematics of vector differential operator, and the meaning of each equation, in a series of future blogs.

The four equations can also be written in integral form, which many people find easier to understand. In integral form, the equations become $\boxed{ \begin{array}{lcll} \iint_{\partial \Omega} \vec{D} \cdot d\vec{S}& = & Q_{f}(V) & (5) \\ & & & \\ \iint_{\partial \Omega} \vec{B} \cdot d\vec{S} & = & 0 & (6) \\ & & & \\ \oint_{\partial \Sigma} \vec{E} \cdot d\vec{\l} & = - & \iint_{\Sigma} \frac{\partial \vec{B} }{\partial t} \cdot d\vec{S} & (7) \\ & & & \\ \oint_{\partial \Sigma} \vec{H} \cdot d\vec{l} & = & I_{f} + \iint_{\Sigma} \frac{\partial \vec{D} }{\partial t} \cdot d\vec{S} & (8) \end{array} }$ The inscription on the front of the statue’s plinth. It reads “James Clerk Maxwell 1831-1879”.