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Homework Statement
Alright, this is a Lab Exercise, so it's light on an actual introduction and data, but I'll do my best to put into words the whole thing. The gist of it is that we have a Vat with water, a millimetre paper at the bottom, and we put two Equipotential surfaces inside. We charge them, and then we take the splinter and measure the V in various places. Here's the "default" version:
Version One: Metal Plaques
As an FYI, it's about 10cm between the plaques, and we measure 5cm on the left, and 5cm on the right, outside of the plaques.
First up, we have to take measurements of V across the x = 0 line (meaning left and right only), outside of the metal plaque on the left, between the two plaques, and outside the metal plaque on the right. Here are the findings:
Then, we have to pick a certain number for V (whatever we want), and find the co-ordinates x & y that correspond to said V. We have to do that three times; once close to the left, once in the middle, and once close to the right. Here's what I have:
Version Two: Metal Cyllinders
Again an FYI, from the center (it's why I drew the x/y axis, to make it clearer, the cross is not part of the "ensemble"), it's about 5cm from each side till we hit the small circle, then 7cm until we hit the big circle, and then we take measurements 5cm outside of it.
In the second version, we do exactly the same things. But, due to the symmetry, we technically only had to measure one side (we chose the right on the First Exercise with the x-axis) and quarter(the one with a certain V; this time we measured the right and down quarter). So, for the V Measurements, we have:
And for the V = Stable one, we have:
This is for the small arch, closer to the small cylinder.
This is for the center arch, inbetween the two cylinders.
This is for the big arch, closer to the bir cylinder.
Alright, so good so far, but here's what I have to do now:
1) Construct the V=V(x) graphs for each Version.
2) Construct the E=E(x) graphs for each Version.
3) Construct the Equipotential and Dynamic Lines
Homework Equations
E→ = -dV/dr*r∧
The Attempt at a Solution
Okay, so, I need help the Graphs. All of them. I'm completely lost and I don't know what to do. We were supposed to do the first 4 there, but for some reason this particular professor has some sort of grudge against my partner, so he kicked us out of the work station, even though we still had about 30 minutes of Lab-Time left. I tried reaching my partner, but he's not responding, so...
Anyway, I could really use some help on all the Graphs. We're supposed to do them on Origin, if anybody has it, so that'd be preferable. I obtained it last week (the less said about that the better; some Uni...), so I don't know how to use it that good just yet, so in case you take that route, I'd appreciate a walk through on what you did. By hand is also acceptable, no problem.
He had us draw some stand-in graphs, which I'll be posting here, but I'd like someone to explain to me WHY they look like this. I missed my whole 3rd Semester (illnesses, hospitals, you name it), so now that I'm on the 4th, and Lab IV is based on curriculum from Physics III, I'm having a bit of trouble.
First up, we have the V=V(x) ones.
This is for the Plaques.
This is for the Cylinders.
For starters, can someone tell me what the graph "means"? Is it just a representation of the correlation of Voltage and the distance? As if we're saying V=f(x)? It's a tad of a silly question, but my book doesn't have Graphs.Then we have E=E(x).
This is for the Plaques.
This is for the Cylinders.
From what I gather, E is kinda like the a to the u when talking about velocity and acceleration. So if say, u is stable, then a is 0, and if u is rising steadily, then a is stable. My problem is that the leaflet's instructions on constructing the E=E(x) are:
"Construct the V=V(x) graph. Be careful, V on top of the conductors (metal plaques/cylinders) is entirely different than in the water (sidenote: the vat contains water). This spot constitutes a spot ofdiscontinuity on the graph. From the sloop of the graph, by bringing the tangent on various places, compute the Electric Field E and construct the E=E(x) graph."
From what I'm getting, he means that I should go to each "section" of V, find the sloop if it's decreasing/increasing, mark that as E, or if it's stable mark E as 0, and the construct a graph that looks like the ones above.
As for drawing/sketching the Equipotential Surfaces & Dynamic Lines, I whipped up some 1-minute "graphs" (no numbers and whatnot, just basic drawings) just to see if my thinking is correct (the Surfaces are the dotted lines, and the Dyanmic Lines are the "straight" black ones):
What I'm curious about here is; the book says that all Dynamic Lines are perpendicular to the surfaces, going from Positively Charged, to negatively. So, like the pic above. However, the Professor told us that the Dynamic Lines would be "parallel" to the Equipotential Surfaces, which I don't see how it works. Did he just make a blunder or am I missing something?
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Look, I realize this whole thing is a bit of a mess, but I could really use the help. The exercise is due on the 22nd, so "technically" tomorrow for me (it's 00:40 on the 21st for me), or really I just have one more day left. Anyway, like I said, I missed the previous Semester and I'm getting my buttocks kicked, so I could greatly use any help to keep going until the summer where I can catch up. So I'd really love it if alongside the graphs you could throw some explanations in.
I'd ask my Lab Partner, but he's working nights to make ends meet, and has failed this Lab once before, so the poor guy ain't of much help. He tries, but he misses emails and such. It's my fault for not uploading it here sooner, but I totally forgot about it since I had other Labs to attend to as well. All in all, it's a Uni that's not really fit to teach, so you guys are my only chances here.
Thanks for the help, it's greatly appreciated!
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