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As an application of micro canonical ensemble, the ideal gas equation and law of equipartition of energy are derived.

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As an application of micro canonical ensemble we show that the fraction of particles in the second level at temperature \(T\) is given by \begin{equation} \frac{n}{N} = \frac{1}{e^{\epsilon/kT} +1}. \end{equation} $newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$

The Maxwell's equations for electrostatic are derived from Coulomb's law which has been formulated based on experiments. This provides initial experimental evidence for the Maxwell's equations. We discuss two applications of Maxwell's equations. The first result is that  the electric field inside an empty cavity in conductors is proved to be zero. The second result is  an  expression for electric stress tensor is derived. The surface integral of the electric tensor gives the force on charge distribution.

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Infinitesimal variation of the action functional is defined and computed for a an arbitrary path \(C\). It is shown that the requirement that the variation, with fixed end points, be zero is equivalent to the path \(C\) being the classical path in the configuration space.

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Gellman-Levi method for computing Noether charge associating with a symmetry transformation is explained, In case of a broken symmetry the Noether generator varies with time and its rate of variation can be computed in a simple manner by the and computing its time variation by this method.