me22b120.tex

\section{ME22B120}
\subsection{Introduction: Casimir Effect }
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948.

The Casimir effect can be understood by the idea that the presence of macroscopic material interfaces, such as conducting metals and dielectrics, alters the vacuum expectation value of the energy of the second-quantized electromagnetic field. Since the value of this energy depends on the shapes and positions of the materials, the Casimir effect manifests itself as a force between such objects.

Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in turbulent water or gas  illustrate the Casimir force.
\footnote{https://en.wikipedia.org/wiki/Casimir_effect}

\subsection{Equation}
The analytic continuation has evidently lost an additive positive infinity, somehow exactly accounting for the zero-point energy outside the slot between the plates, but which changes upon plate movement within a closed system. The Casimir force per unit area F/A for idealized, perfectly conducting plates with vacuum between them is
\begin{equation}
\frac{F}{A}=-\frac{d}{da}\frac{<E>}{A}=-\frac{\hbar c\pi^2}{240a^4}
\end{equation}
where 
\begin{itemize}
    \item $\hbar$ is reduced plank constant
    \item c is speed of light
    \item a is distance between two plates
    
\end{itemize}
\footnote{https://en.wikipedia.org/wiki/Casimir_effect}
The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of $\hbar$ shows that the Casimir force per unit area F/A
 is very small, and that furthermore, the force is inherently of quantum-mechanical origin.
\subsection{Application}
In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics it is significant in some aspects of emerging microtechnologies and nanotechnologies.
 Name: Deepmoy Rudra Sarma \\
\ Github id: catrplr