# Homework Help: Help to solve electric field lines in a dielectric

1. Sep 27, 2008

### sairajan

Hi all,

I am trying to solve numerically as well as model the electric field lines coming out of a electrode (not a point charge) in a dielectric medium. ANy suggestions would be greatly beneficial

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_ seperated by d + seperated by d _

---> Di electric medium + positive charge
_ Negative charge

_ seperated by d + seperated by d _ Field lines are from + to - and are elliptical

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Last edited: Sep 27, 2008
2. Sep 27, 2008

### Redbelly98

Staff Emeritus
I would solve for the voltage with eg. LaPlace's equation (or was it Poison's? Sorry, it's been a while for me), then use
perhaps with a Runge-Kutta algorithm.

3. Sep 27, 2008

### sairajan

Hi,
thanks. How do you use Laplace for solving. Thanks. Any suggestions are greatly appreciated. Do you have any links online which tells that. Thanks

4. Sep 27, 2008

### Redbelly98

Staff Emeritus

A good reference book is Numerical Recipes in C, or Numerical Recipes in Fortran, by Press, teukolsky, Vetterling, and Flannery. You can look in the section on Relaxation Methods in the chapter on Partial Differential Equations.

But I will warn you that you can spend a lot of time writing code, perhaps more than you want to. If this is a work-related project, buying some commercial software that models E-M fields is a better way to go. For example:
http://www.ansys.com/Products/emag.asp [Broken]

Last edited by a moderator: May 3, 2017
5. Sep 28, 2008

### sairajan

Hi,
very many thanks for your reply. I am actually struck on how to solve the laplace equations. I want to have a numerical solution for this problem. Should I start with electric field due to a line charge. Where can i find that material ?
Thanks

6. Sep 28, 2008

### Redbelly98

Staff Emeritus
I don't see how that would help. It looks like flat electrodes in your figure.

Solving Laplace's equation numerically:
http://physics.exeter.ac.uk/teaching/CDHW/EM/CW960313-2.pdf
which is the first hit (out of 55,000) listed at

I'll reiterate, this gives the potential, not the electric field. Also, the dielectric boundary complicates things somewhat and I imagine you need to set up the equation differently along the boundary.

You'd still need to get the E-field once you have the potential.

If others in here have better suggestions, feel free to jump in ...

7. Sep 28, 2008

### marcusl

I'm afraid if you haven't studied electricity and magnetism, you could be lost in this problem. You need at least solutions to the Laplace equation, potentials and fields, and orthogonal funcitons. Complex variables would be helpful, as noted below. You might start with a standard E&M book like Griffith's, or the beautiful but not so well known one by Mel Schwartz.

There is a nice technique that probably can give you an analytic solution to this problem. You transform this problem to a parallel line (e.g., parallel plate) geometry with a conformal transformation, solve it analytically there, and transform the solution back to the circular geometry. I can't remember the transformation off the top of my head--I think it's the bilinear transform. Smythe's book Static and Dynamic Electricity covers the techniques you need, although it's not a beginner's book.

Last edited: Sep 28, 2008