Air-filled parallel-plate capacitor question

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SUMMARY

An air-filled parallel-plate capacitor with a desired capacitance of 0.4 F and a plate separation of 0.7 mm requires a specific surface area calculation. The capacitance equation C = (Eo * A) / d, where Eo is 8.85e-12 C²/N·m², is used to determine the area A of each plate. A common misconception is to divide the calculated area by two, which is incorrect as A represents the area of a single plate. The correct approach is to use the full area derived from the equation without division.

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  • Understanding of capacitance and the formula C = (Eo * A) / d
  • Familiarity with the constants involved in electrostatics, specifically Eo (permittivity of free space)
  • Basic knowledge of unit conversions, particularly between square meters and square miles
  • Ability to perform algebraic manipulations to isolate variables in equations
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Students in physics or electrical engineering, educators teaching capacitor theory, and professionals involved in circuit design or electrostatics applications.

Aerospace
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An air-filled parallel-plate capacitor is to have a capacitance of 0.4 F.
If the distance between the plates is 0.7mm, calculate the required surface area of each plate. Answer in mi^2.

Okay, so I used the Capacitance equation where C=(EoA)/d where Eo is a constant 8.85e-12 C^2/N.m^2
and A is the Area of the plates and d is the plate separation.
So I plugged in the numbers, found the area and divided it by two to get the area of each plate. I'm getting the wrong answer and I don't know what I'm doing wrong.

If anyone could please help, it would be appreciated. Thank you.
 
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Why did you divide it by 2? The A is your final answer
 
Originally posted by NINHARDCOREFAN
Why did you divide it by 2? The A is your final answer
Probably because the textbooks are quite pathetic when it comes to introducing capacitors (among other things). They say things like, "the area of the plates," and it is only natural for some students (IMO the more rigorous ones) to interpret that as the total area of both plates.

Aerospace,
The A in the equation is the area of each plate, not the total area of both plates. Don't divide by 2.
 

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