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/sci/ - Science & Math

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4433252 No.4433252 [Reply] [Original]

Need some help on my homework :(

Question: The upper and lower conducting plates of a large parallel-plate capacitor are separated by a distance D and maintained at potentials V_0 and 0, respectively. A dielectric slab of dielectric constant 6.0 and uniform thickness 0.8d is placed over the lower plate. Assuming negligible fringing effect, determine the following by solving Laplace's Equation:

a) the potential and electric field distribution in the dielectric slab,
b) the potential and electric field distribution in the air space between the dielectric slab and the upper plate, and
c) the surface charge densities on the upper and lower plates.

This is what I understand this problem to look like, and I know laplace's equation is ∇^2 V=0, but without a potential at V, I don't know how to solve this. Help?

>> No.4433264

Assume V as 1

>> No.4433273

>>4433264
Can you elaborate as to why that is?

>> No.4433296

>>4433273

Not the other poster, but...

What I think he is saying is that you should give your answer in terms of the other variables. Choosing one is easiest.

>> No.4433330

I'm still not quite understanding what you are saying :(

>> No.4433367

Please. If anyone can help me any more than this, I would be grateful.

>> No.4433489

Okay, so I have this so far:
V=(V1(y) = C1y+C2, 0 < y < .8d
(V2(y) = C3y+C4, .8d < y < d

V1(0) = 0 = C2
V2(d) = V_0 = C3*d+ C4 => C4 = V_0-C3*d
V1(.8d) = V2(.8d) = C1*(.8d) = C3*(.8d)+(V_0-C3*d)
but I am missing an equation, cause I have 4 unknowns, not 3 :(

Additional help would be helpful.

>> No.4433526

Please, someone help. I don;t know where this last boundary eqn is!

>> No.4433536
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4433536

Part 1/2

>> No.4433545
File: 377 KB, 2550x3300, img003.jpg [View same] [iqdb] [saucenao] [google]
4433545

Part 2/2

Will keep an eye out to see if you're still having some trouble. If you see a mistake, my bad, it's pretty late. :) But hopefully that helps.

>> No.4433613

>>4433536
>>4433545
Good sir or madame, If I could Hug you I could, but since I can't, I will simply bid you thanks and give you an internet, as with this, I have finished the problem.

>> No.4433649

>>4433545
>>4433536
If you're still here, I have a question that isn't clarified very well in my book.

In problems like these where it isn't expressly stated to use Laplace's or Poisson's Equation, how do you decide? My book says when there is no free charge, but I am having a hard time understanding what that means.

>> No.4433679

When there is a volume charge enclosed in the given material(s), think Poisson's eq. When there is no indication of a volume charge in the problem, think Laplace's eq.

>> No.4433680

>>4433545
did you seriously fucking help this kid with EM1 homework.

>> No.4433687

>>4433679
That makes sense. thank you sir or madame

>> No.4433740

What class is this? Looks almost like physics II with the dielectric/parallel cap part but gets a little more complex with Poisson/Laplace equations.

>> No.4433870

>>4433740
This is an electromagnetic theory class. We're moving into magnetic fields and such after spring break

>> No.4433896

>>4433870

Neat! We're also moving in that direction...but it's still physics 2.

Are you in Europe? Major is? What year are you?

>> No.4433922

>>4433896
I am a Junior in Computer Engineering at the University of Wyoming (not Europe, sry :)