Starting image - this is messy and confusing. It's not clear what it's purpose is. A single image of a capacitor might be helpful once you introduce it.
First couple paragraphs - I would lead with something a little less brow-beating xD. Capacitors have a super interesting and fun history in the Leyden jar, you could try talking about that. It used to be everyone's favorite pastime to take a glass jar, wrap either side in foil, and then add some charge to it by rubbing a rod with some fur or something. They are also ubiquitous - they are how defibrillators work (charge up a bunch of capacitors and then dump all that charge). You could then talk about bigger jars being able to store more charge, and ask then segue into something about capacitance being the idea that describes charge storage.
Third paragraph - current is the instantaneous flow rate (spatial average). I would strike the word average. We're not usually interested in the total charge, but sometimes we are.
I would make the digression about constant capacitance shorter.
The finite-difference digression could be used as a good example - when you have a constant current, what is the voltage that develops across the capacitor? I wouldn't make it part of the main text, but it's so useful it deserves maybe 2 examples.
In general, at this point students haven't had a chance to do any circuits practice and throwing time-dependence into the mix I think would just be confusing. I would move this section to later in the course once we have covered plenty of DC circuit techniques and students have had time to get very comfortable with those.
I don't come away from this understanding what capacitors are, why they are used or useful, or how to use them. What's the story you are trying to tell about capacitors? What are we trying to find when we analyze them? There's some math here (a differential equation and an integral one), but how do I use it? When do I use the differential form, and when do I use the integral form? What do both of them mean?
Starting image - this is messy and confusing. It's not clear what it's purpose is. A single image of a capacitor might be helpful once you introduce it.
First couple paragraphs - I would lead with something a little less brow-beating xD. Capacitors have a super interesting and fun history in the Leyden jar, you could try talking about that. It used to be everyone's favorite pastime to take a glass jar, wrap either side in foil, and then add some charge to it by rubbing a rod with some fur or something. They are also ubiquitous - they are how defibrillators work (charge up a bunch of capacitors and then dump all that charge). You could then talk about bigger jars being able to store more charge, and ask then segue into something about capacitance being the idea that describes charge storage.
Third paragraph - current is the instantaneous flow rate (spatial average). I would strike the word average. We're not usually interested in the total charge, but sometimes we are.
I would make the digression about constant capacitance shorter.
The finite-difference digression could be used as a good example - when you have a constant current, what is the voltage that develops across the capacitor? I wouldn't make it part of the main text, but it's so useful it deserves maybe 2 examples.
In general, at this point students haven't had a chance to do any circuits practice and throwing time-dependence into the mix I think would just be confusing. I would move this section to later in the course once we have covered plenty of DC circuit techniques and students have had time to get very comfortable with those.
I don't come away from this understanding what capacitors are, why they are used or useful, or how to use them. What's the story you are trying to tell about capacitors? What are we trying to find when we analyze them? There's some math here (a differential equation and an integral one), but how do I use it? When do I use the differential form, and when do I use the integral form? What do both of them mean?