I, Scientist | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Afterword
I have always wanted to be a scientist ever since I was in elementary school. But it was only after I took the first physics course in high school, I was instantaneously hooked and chose physics specifically as my future profession. I distinctly remembered learning Newton’s three laws of motion for the first time, and thus gained the ability to predict how objects move under various combinations of forces. I learnt how a pendulum or vibrating spring oscillates sinusoidally with the exact same frequency despite a change in the mass of the load; or how two objects near the ground are affected equally by Earth’s gravity and tracing out the same a parabolic trajectory despite their differences in mass. Looking back, it was this kind of “preciseness” that physics provided (when other sciences didn’t) that made me walked on this path rather single-mindedly.
In high school, my fascination over physics was quite a double-edge sword. On one hand, I was learning with the amount of stimulation like nothing I have experienced; on the other hand, I suffered badly from the staleness of the examination system. I hated being asked by our teachers to practice calculations over and over just so we could finish the exams on time, get high grades, and have higher chance to get into one of the top universities for college. Luckily (or rather unfortunately depending on the point of view), I could escape to my own physics world anytime, at least momentarily.
In high school, among all physics puzzles I created for own curiosity, there were three problems—each involves a different type of force—I remembered most clearly. The forces they involve are constraint force, tension force, and electric force respectively*.*
After we learnt the notions of potential and kinetic energies, the first problem we were asked to solve was a block on a ramp with initial height $h$ at zero velocity $v_0=0$. The question: what is the final velocity after the block reaches the flat surface? The solution is to use conservation of total energy, $mgh=\frac{1}{2}mv^2$, to compute the final velocity $v$. This was supposed a 1-minute problem, yet I couldn’t let it go for days. For the equation suggests that there is only gravity $g$ involved, but mysteriously the earlier velocity along the incline largely moving downwards eventually turned horizontally completely exiting the ramp. The fact that the block changed its direction implies a different force exists in addition to gravity during the whole movement. I later learnt that such a force is called “constraint force”, and it doesn’t change an object’s kinetic energy because the force acts perpendicularly to the movement. But I learnt the hard way that such a fact doesn’t come easy; not without the concept of calculus which I would fully learn a couple of years later in college.
Equally mysterious as constraint force is tension force, and the source of such mystery again came from the ideas of calculus. I remembered feeling extremely excited about learning surface tension in our senior physics course, and was amazed by how precisely the convex shape of water surface near the inner wall of a glass cup can be calculated with the knowledge of tension force among water molecules and adhesive force between water and glass. During the time of learning this subject, I would imagine myself as one of the water molecules near the liquid surface and being either close to the glass wall, slightly far away, or slightly deeper into the liquid bulk, etc., in order to work out the precise forces acting on my body that would mutually balance out.
Similar to a collection of water molecules creating a macroscopic phenomena near the surface, a collection of electrons also form a new kind of macroscopic physical quantities like capacitance, inductance, and resistance. I remembered first time learning to compute the total electric energy from all charge particles (infinitely many but finite in their total charge) uniformly distributed on a spherical surface. This electric energy can be macroscopically computed:
$$ E_{el}=\frac{1}{2}CV^2 $$
where $C\sim R$ with $R$ being the radius of the sphere, and $V\sim Q/R$ is the voltage on the surface. To me, this equation is very mysterious because there is another way to express the total energy microscopically:
$$ E_{el} \sim \sum _{i=1}^{n}\frac{( n-i) q\cdot q}{R} $$
where the sum of charge fragments equal to the total charge $Q=nq$ with $n\rightarrow\infty$. I wrote down this equation from the following reasoning: