Practice:Physics visualization

=Merits and Demerits of Visualization in Understanding Physics=

Introduction
Why visualization is considered as an effective tool in understanding concepts of physics? A simple and common reason is our dependence on our eyes for the gain of information in comparison to other mode of perception like listening, smelling and touching. Use of graphs in mathematics is a manifestation of our lack of understanding of the beauty of mathematical equations and our mind’s inability to retain the algebraic expression in our mind for long. That’s why Java applets describing various phenomenon in Physics like simple harmonic motion, wave, oscillations ,quantum tunneling, and very recently quantum teleportation are so popular.

some exmaples
If somebody asks us what is simple harmonic motion, a person with a non Physics background will see bob of a pendulum oscillating in his mind .But what does a trained physicist sees in his mind ?He sees the second order differential equation in his mind. In this way he understands the deeper meaning attached with the S.H.M. Let’s take another probing question. We know that an L-C circuit executes SHM. But what is actually moving or varying periodically? In this charge in capacitor is growing and decaying simple harmonically or sinusoidally .The above is an example where a system (LC circuit)is just lying there in space, but a physicist knows it is a system in which a SHM is going on and exactly in what sense. Now if you take help of graph ,both displacement of bob from equilibrium in simple pendulum and magnitude of charge in capacitor, put on y-axis and time put on x-axis shows a similar pattern on the graph, that of sinusoidal curve. Power of visualization! But what is the underlying structure due to which both quantities, displacement of bob and charge on capacitor, varies in similar fashion wrt time? Try to find answer by visualizing. Here it is of no help. It fails. But if you begin analyzing behavior of both systems by setting up a differential equation, you will land up with same differential equation, popularly known as equation of SHM. Now we can appreciate the role of mathematics in general and calculus in particular. So far we have considered the situation in which two different quantities were varying sinusoidally w.r.t. “time” only .Now arises the question does all physical quantities in SHM has to vary wart time only, why not some other variable like “displacement in space ”. Try to visualize the situation. You will again be in difficulty.

Role of mathematics
Now role of function (which will play role of any physical quantity) and its variables come into picture. More interestingly, is there any physical quantity which varies simultaneously both in time and space simple harmonically? Answer is in affirmative .It is the propagation of wave, e.g. electric field vector of plane polarized light propagating in space varies sinusoidally both in time and space. How to visualize? We will compare graphical method (visualizing) and analytical method to understand this phenomenon in later part of this article.