Not-So-Parallel Plate Capacitor

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Enemy0fGods
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1. You have fabricated a parallel plate capacitor in your work shop, but the square metal plates end up not being exactly parallel to each other. They form an angle [tex]\alpha[/tex]. The plates, size L, are held at constant electrical potentials, V1 and V2, corresponding to an electrical potential difference [tex]\Delta[/tex]V = V1 - V2. Plate 1 holds a +Q charge while plate 2 holds a -Q charge.

I'm done with parts a-c, but I need help with these:

d: Find the total charge carried by the plates (Hint: This requires an integral).
e: Show that the value of the capacitance of this capacitor is C = ([tex]\epsilon[/tex]0L)/[tex]\alpha[/tex] *ln(b/a). Does this have all the usual attributes of a capacitance?


[PLAIN]http://img19.imageshack.us/img19/220/unledeyr.png

2. Homework Equations : Already listed one, and E=V/d, and the rest I don't know.



3. The Attempt at a Solution : I don't really have an attempt, I'm stuck, all I know is I'm suppose to use an integral with part d, which is already given anyway.

Thanks for any help.
 
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Out of curiosity, what were parts a - c ? & what were your answers to those?
 
2. Homework Equations : Already listed one, and E=V/d, and the rest I don't know.

What do you mean by "d" ? The distance between the plates varies with x.
 
for (e)
Diagram of two wedge-shaped conducting plates meeting at a point 0 at angle alpha, with plate V1 charged +Q and plate V2 charged -Q; a thin red strip of width dx sits at distance X from the apex, with labels a, L and b marking lengths along the plates.

consider the part of capacitor inside red rectangle ... it is also a capacitor.
find capacitance of this capacitor in terms of variables you know and x,dx ...
then integrate ...
 
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  • Diagram of two wedge-shaped conducting plates meeting at a vertex 0 with angle α, labelled V1 at +Q on top and V2 at -Q below, with x axis and a thin red strip of width dx at distance X from 0; distances a and b and length L are marked.
    Untitled.png
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and for d
question itself says plate 1 has charge Q and plate 2 has charge -Q
so total charge would be 0 right?
 
cupid.callin said:
and for d
question itself says plate 1 has charge Q and plate 2 has charge -Q
so total charge would be 0 right?

Perhaps the question meant the charge on each plate in terms of potentials and capacitance.
 
but why would question ask that
for (d) first you should do e
so d must be placed next to e ... which it is not