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PHY 101: Vector Integration

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What is Integration? Integration can be thought of as a continuous analogue of sum (\(\sum_{ }^{ }\)). We integrate or simply add infinitesimal small quantities together to form a continuous chain. Integration can be of 3 kinds rather I would call it 3 ways of integration. Linear, Area and Volume way. To show what each of them looks like here is a visual representation: $$\begin{aligned}& Linear \hspace{1mm}integration:\int_{ }^{ }f(x)dx\\ \\ &Area\hspace{1mm}or\hspace{1mm} surface\hspace{1mm} integration: \iint_S f(x,y)dxdy \\ \\ & Volume \hspace{1mm} integration: \iiint_V f(x,y,z)dxdydz \end{aligned}$$ You might have already noticed that the number of integration symbols (\(\int_{ }^{ }\)) increases with the increase in the number of variables. Hence, most books adopt the notation of calling these single, double and triple integrations. We at physics are creatures of simplicity and thus have kept it easy to remember. Let us talk about each in some detail! Single or Linear...
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The Particle paradox of Quantum Duality

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Duality of Particles Early 1700s: In early times people had the notion of particles namely photons or light as collectively to be either of wave nature or particle nature. Many scientists conducted various experiments to prove the existence of light as one of those natures. But one thing that they all observed was that light was acting as both particle as well as wave nature. This seemed moot for the genius minds of the time. How can light be a wave and a particle simultaneously? That is simply not possible. To prove the particle nature of Light: The photoelectric effect was considered to be sufficient proof. The experiment basically shows that when a light of a certain frequency is greater than the threshold frequency of the material upon which it is incident, it causes the surface to give off electrons. The number of these electrons often called photo-electrons is proportional to the intensity/amplitude of the light. The excess energy is then transferred to the electrons as their kin...
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