Summer of Math Exposition

I really liked how all of the formulas were made understandable by building them piece by piece throughout the video. The visual explenation of the equations at every step and at the end of the video, in my opinion, really helps the viewer better understand and get a deeper intuition for the concept. One thing that could be changed is that the video defaulted back to the donut shop image during crucial steps of the derivation which could make it harder to understand. The same principle applies for some moments where the steps were described by the narrator, but were only shown on screen later in a rafale of equations. Overall, great job!

This video would benefit from a short introduction reminding the audience how electric fields and Coulomb’s law work. Also, the focus is on the mechanics of calculating the answer, rather than any underlying intuition, so it feels like something to watch after working through the problem myself instead of an explainer in its own right.

Is there a way to more simply explain this? You got me lost time to time

Motivation (1) - unclear why I would care about the E fields on a half-ring

Clarity (7) - easy to understand

Novelty (2) - Not unique at all, a very common derivation

Memorability (2) - although it was easy to understand, didn’t provide any new insight or novelty so it’s not any more memorable than the standard derivation.

I wish it came back to the donut at the end. I think I eventually realized that the “ring of charge” has no thickness - it’s just a circle, so the the ring fits on a 2D plane. The donut is more like a torus, so I wasn’t sure if the “charged donut” had all of its charge on the surface of the donut, or if it occupied the volume of the donut. Either way, a torus is definitely a 3D shape. Also, while the graphs of the E-field at the end where neat, they seemed to be the E-field of the z-axis. Would have been nice to have an animation more like the picture the donut at the very beginning, where it shows the electric field lines in full 3D space, not just a representation of the E-field as experienced by the z-axis.

I really liked the start with the doughnut shop, but what came after it fell to sort of a “death by a thousand cuts”: from little annoyances like consistently saying “E field” rather than just saying “electric field” or having both lowercase $r$ and uppercase $R$ refer to radius, to things like equating vectors to their magnitudes (which are scalars) and using $\phi$ to refer to both the the angle that $dQ$ is at and the total angle in the half-circle… this leads to you mentioning that your definition of $\lambda$ would introduce a $\frac1{\phi}$ term you’d have to integrate but then you pull it out like a constant… the editing is also not really consistent… your recordings are clear, and you got some key points across about the symmetry in the problem, and the graphs at the end were neat, but there are a lot of other things here where I think more care was needed.

Motivation was not very clear to me. The visualization of vectors were quite understandable. I did not found the formulas interesting enough to follow the rest of the video.

Small detail: when writing things like “charge” in math formula, usually this is done with normal letters, for example in LaTeX $\mathrm{charge}$, because $charge$ looks like a product of c, h, a, r, g, and e.

Great video, but I dont think this would help high school students but may only undergraduates or graduates.

An interesting video on general physics that is not commonly seen on the internet. It calculates the electric fields generated by arcs of different lengths on the axis of symmetry of the circle to which the arcs belong. I thought the explanation of the calculation was good, but I think it would be nice to add a little more dynamism to the animations of the mathematical demonstrations. Or perhaps it would be better not to explain the mathematical calculation in such detail, but rather to focus on certain important aspects that allow us to understand how the mathematical expressions are obtained. Beyond this, I found the graphical demonstrations of the results to be very good and very clear to understand. Overall, I thought it was a good video. Congratulations!