Can somebody for the love of humanity and genuine curiosity explain why does the voltage between 2 oppositely charged ends of a progressively depolarizing cell peak when the wave reaches the middle of the cell as shown in the picture? And why does it begin to fall after that? I've tried to reason this out with everything that I know or had been taught about dipoles and charges and currents and whatnot, but I can't convince myself that I understand why this is happening. Please explain without using lines like "that's because that's where they are the most different"....coz such lines are the least helpful of all. Thank you.
that's because that's where they are the most different
is exactly right. You have two electrode sites, "blue" and "pink". Voltage is an electrical potential difference.
If you sum up all the charges near "blue" and sum up all the charges near "pink" (where "near" means that closer charges matter more than those further away), in either your upper right or lower left plot, you'll get the same sum at blue and pink, so pink-blue = 0 = voltage.
If you sum up all the charges near "blue" in the top left plot, you'll get a negative number, if you sum up all the charges near "pink" in the top left plot you'll get a positive number.
When you "flip" a charge, it's going to affect both blue and pink, but it will affect the one it's closest to more. Therefore, if you were trying to design a scenario with the biggest difference, you'd want all the charges closest to blue to be opposite the charges closest to pink.
If you're somewhere in between the top two plots, say, take one of the positive charges to the right of the green arrow near pink and make it negative, you'll make both red and pink more negative. If the position of this charge were equally between the two electrodes, it would affect them both equally, and there'd be no difference in voltage. However, everything to the right of the green arrow is closer to pink, so any change there affects pink more than blue. That means that changing one of those positive charges to negative makes the positive pink electrode less positive by a larger amount than it makes the negative blue electrode more negative, so the difference is smaller.