What is the Work Required to Increase Separation of a Parallel Plate Capacitor?

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SUMMARY

The forum discussion centers on calculating the work required to increase the separation of an isolated parallel-plate capacitor from 1.2 mm to 4.5 mm while maintaining a constant charge of Q=1.4x10^-5 C. The capacitance at the initial separation is given as C1=3.1x10^-11 F. Participants discuss the formulas for capacitance and potential energy, ultimately determining that the work done is W=192.76 J after calculating the potential energies at both separations. The correct capacitance at 4.5 mm is found to be C2=8.26x10^-12 F.

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  • Understanding of parallel-plate capacitor theory
  • Familiarity with capacitance formulas, specifically C=ε₀A/d
  • Knowledge of potential energy in capacitors, U=(1/2)(Q²)/C
  • Ability to perform unit conversions, particularly between millimeters and meters
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Students studying electromagnetism, electrical engineers, and anyone involved in capacitor design or analysis.

  • #31
sw1mm3r said:
thats the formula i was talking about

c2=(3.1x10^-11 F)/3 doesn't give you c2=8.26x10^-12F.
 
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  • #32
no look c1/c2=d2/d1

(3.1x10^-11)/c2=.0045/.0012

c2=8.26x10^-12 so c2 is obviously not c1/3
 
  • #33
OOhhhh. You are talking about c2=(1.2/4.5)*c1. The 1.2 was a typo. There's no '1.2' in the problem anywhere. I apologize for that. It should have been 1.5. You really haven't understood anything of this, have you?
 
  • #34
1.2 is in the problem its 1.2 mm... and i have understood a good chunk of stuff i just got confused on the last part
 
  • #35
Hah. You're right. I substituted the 1.5 for 1.2 way back. Apparently I'm the one who's confused. 34 posts and you lose track. Sorry again. I think you've got it right.
 
  • #36
damn and i was tryin to figure out where i went wrong... kool sounds good i understand it then
 
  • #37
sw1mm3r said:
damn and i was tryin to figure out where i went wrong... kool sounds good i understand it then
I will rewrite my post.
C1 = εοA/d1
In the second case
C2 = εοA/d2

C1/C2 = (εοA/d1)/(εοA/d2)
= d2/d1
Substitute the values of d1, d2 and C1, and find the value of C2.
Using the formula for energy, find the energies in C1 and C2 and find the difference.
 
  • #38
That's perfect. Sorry again if my false recollection that one of the d's was 1.5mm instead of 1.2mm was what was throwing you off. Oh, that's you rl.bhat, thought is was sw1mme3r. Maybe time to quit while I'm not too far behind.
 
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