How Do You Design a Parallel Capacitor Given Only Electric Field Intensity?

[skyT]

do u all mind sharing with me what are the steps needed/ the procedures to design a capacitor? Its like I've been given only its electric field intensity. And is required to find out the capacitance... mind chip in some ideas for me? btw, I am designing a parallel capacitor.

relevant equations :
electric flux density, D = epsilon * electric field intensity + polarisation vector
polarisation vector = epsilon*electric susceptibility*electric field intensity

the attempt at a solution :
I've manage to solve the above and I am now stuck at the Gauss' law equation...
where
E=Q/(4*pi*r^2*epsilon)
can i know what does the radius stands for? is it the radius of a charge? or the radius of the capacitor? is it fixed or we can determine it ourselves? please help...

 

[mheslep]

do u all mind sharing with me what are the steps needed/ the procedures to design a capacitor? Its like I've been given only its electric field intensity. And is required to find out the capacitance... mind chip in some ideas for me? btw, I am designing a parallel capacitor.

relevant equations :
electric flux density, D = epsilon * electric field intensity + polarisation vector
polarisation vector = epsilon*electric susceptibility*electric field intensity

the attempt at a solution :
I've manage to solve the above and I am now stuck at the Gauss' law equation...
where
E=Q/(4*pi*r^2*epsilon)
can i know what does the radius stands for? is it the radius of a charge? or the radius of the capacitor? is it fixed or we can determine it ourselves? please help...

You essentially need two pieces of information to get started:

1. C = \varepsilon_{r} \frac{A}{4\pi d}, where:
A is the area of conductors
d is the distance between them
\varepsilon_{r} is the dialetric constant of the materials separating the plates. The dialetric constant for air is about one, for a common commericial capacitor material such as Barium Titanate the value can reach 10,000.

2. The breakdown voltage of the particular material you use to separate the conductors. The breakdown voltage of air for instance is about 3 million volts per meter of separation (3000 volts per mm and so on).

The above concerns the primary physics.

Then there are the practicallities: How long will your dialetric material last? Will it chemically react with the conductors over time? If and when an overvoltage breakdown occurs, will the device fail explosively? What kind of container will you use? Will the container prevent other materials from entering the capacitor over time and changing its performance?

 

[skyT]

wow. That sounds like a lot of work. Is it possible to prove that both Laplace Equation and Gauss' Law can be used to get the same value of capacitance for a spherical capacitor?

 

[mheslep]

wow. That sounds like a lot of work.

Well not if you want to build a simple air capacitor for an experiment or demonstration, as opposed to practical use.

Is it possible to prove that both Laplace Equation and Gauss' Law can be used to get the same value of capacitance for a spherical capacitor?

The equation above for capacitance is independent of the geometry you chose. If you want to look into the derivation of capacitance from fundamental electromagnetic principals, perhaps the physics sub forum is a better place to ask, though I expect the wikipedia pages on capacitance already answer your questions.