# The Electric Field of a Cylindrical Capacitor?

1. Jul 24, 2008

### seekingaeolus

1. How do we calculate the electric field of a Coaxial Cylindrical Capacitor??

That is one question, the other is:

Is the field strength E the same at all locations of a uniform electric field at any point between the plates or electrodes of a parallel plate capacitor, and or a cylindircal capacitor???

2. Gaussian Symmetry?

3. Not sure....found the field of a point charge....

Thanks a lot

2. Jul 25, 2008

### cryptoguy

For your first question, yes you use Gauss's law. Now imagine for a coaxial capacitor, the inside of it has a charge +Q and the outside has a charge -Q. Which of these (or both) contribute to the electric field in the capacitor according to gauss's law?

Now with this, you should be able to figure out the electric field.

3. Jul 29, 2008

### seekingaeolus

Still very lost.

When I looked at Gauss's law, I gathered that the elctric flux $$\phi$$

is equal to E0 *(2*$$\pi$$*LR3/r2

And I also found that the Electric field of a long charge wire is equal to

E = $$\lambda$$/2*$$\pi$$*$$\epsilon$$0Lr

???

I'm not sure how to use Gauss's law here.

From my understanding, if my inner cylinder has a net positive charge of Q and my outer cylinder has a net negative charge -Q then my electric field will extend from the inner cylinder to the outer cylinder, increasing in strength from radius R to radius r

ie from the radius of my inner cylinder to the radius of my outer cylinder.

However. when I draw the gaussian surface to represent this, I do not know where to begin the cylinger to determine the charge enclosed. This could be for any abitrary cylinder value ranging from 1/2 in to 6 in depending on what diameter pipe I use....

I realize that in order to maintain field strength integrity to the narrowest bandwidth, or sharpest, most consistant field strength, then the distance between the two electrodes needs to be as close as practically possible. However, I am unsure as to what kind of field strength changes I can predict per the size of the electrodes. In other words, how different will the field be if the pipes are larger in diameter or smaller in diameter...or will that even affect the field strength inside the capacitor??

Can you help me with this?

4. Jul 29, 2008

### Defennder

The Gaussian surface should be in the shape of a cylinder for you to be able to exploit symmetry. So what does Gauss law applied to that Gaussian surface tell you about the the strength of the electric field?

What pipes are you talking about?

5. Jul 29, 2008

### seekingaeolus

I am making a coaxial cylindrical capacitor with a dielectric constant of roughly 87.9

The cylinders are stainless steel tubing about .1 meter long, concentrically spaced approximately 1 mm apart (as of right now. depending on what kind of results I get from this calculation, the spacing might be different)

I am trying to find a relationship to associate electric field strength as a function of capacitance. The charge Q plays an important role as the bridge between field strength and capacitance, with applied voltage being an independant variable that I consider as something I can vary to get the proper output.....ie somewhere between 8 and 14 volts....unless a coil is needed to jump up my voltage higher.....

With luck I can find the relationship, therefore finding a capacitor design that will give me the necessary field strength within certain design constraints and parameters.

6. Nov 15, 2010

### killswitch_on

Hi

Im not sure what your standard of education is, but you could very easily do a steady state analysis of the cylindrical capacitance on ANSYS to give you all the results you are looking for.

Pick a 2D plane 121 element and draw the cross section of the capacitor, that is an annulus. Material properties - electromagnetic - relative permittivity - 'enter value'
apply voltage loads on the 2 circles on the cross section and solve.

Hope that helped.

Can u please tell me what application you are using this for?

Cheers
Good luck!