Posts

Showing posts from February, 2024

PHY 101: Vector Integration

By -
Image
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...
1 comment
Read more

The Ultraviolet Catastrophe: Failure of Classical Physics

By -
Image
Have you ever seen a hot iron rod? Or a Blacksmith hammering a piece of hot metal? You must have noticed then that those iron pieces glow or emit light. It was very well established in {some date} that Light is an electromagnetic wave i.e. made up of electric and magnetic field. While we had an idea of what light is made of, physicists did not know why hot objects emitted it back then.  How do hot objects emit light? When we heat a piece of iron, it first glows red, then orangish-red, to yellow ultimately leading to white. The brightness or intensity as it seemed was directly proportional to the increasing temperature, for simplicity's sake.  However, what they wanted to know was how the intensity varied with the wavelength of the light. What you need to understand is that for an object to emit radiation(visible), it need not be so hot to become luminous. All objects emit radiation in the Infrared spectrum(remember the rbg scale which tells us the temperature of the object), t...
1 comment
Read more