# Electrostatics/Electrokinetics and Joule Effect **URL:** \ **Category:** Feature Requests\ **Created:** [May 18, 2025, 3:25am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712 "2025-05-18T03:25:05Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 18, 2025, 3:25am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/1 "2025-05-18T03:25:05Z")
Hi Matej, According to the manual, seems like Don Guido is suggesting to perform electrostatic calculations as a special case of thermal calculations. To do that one should apply the analog relationships between electrical and thermal quantities. Those are described in Table 13: Correspondence between the heat equation and the equation for electrostatics (metals and free space) I’m working on that for a simple case with good results up to now but I’m missing some things. To compute the Electric Field vector, Prepomax should be able to compute the Gradient of the Temperature Field (in fact – gradient ) I would like to request the possibility to add the Gradient of a Field as an Output to keep going. Ex=−∂T∂x,Ey=−∂T∂y,Ez=−∂T∂z. ![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/7/7f9540f61e7bb2e28c0bc9c591e02b696478aa2c.png) ![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/6/6bd5a5b542114fb191645db514e2fb9d5f88b018.png) Regards ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 18, 2025, 7:10am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/2 "2025-05-18T07:10:22Z")
Recently, support for electrostatic analyses with CalculiX was added to FreeCAD FEM. More types of EM simulations will follow but there are certain limitations. Elmer is way more capable in terms of EM and we have a new validated Joule heating example using that solver in FreeCAD. ---
**Author:** ![Matej](https://avatars.discourse-cdn.com/v4/letter/m/a698b9/32.png) [@Matej](https://prepomax.discourse.group/u/Matej)\ **Post date:** [May 18, 2025, 1:36pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/3 "2025-05-18T13:36:02Z")
So the gradient should be added as a post-processing option for user created field outputs? ---
**Author:** ![belov](https://avatars.discourse-cdn.com/v4/letter/b/bc8723/32.png) [@belov](https://prepomax.discourse.group/u/belov)\ **Post date:** [May 18, 2025, 6:25pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/4 "2025-05-18T18:25:55Z")
Gmsh&GetDP has user-friendly predefined templates for magnetostatics, electrostatics and elastics (stress&strain) 2D/3D ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 18, 2025, 6:54pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/5 "2025-05-18T18:54:38Z")
I’m not sure. I guess in Pre-processor, so the different components are later available in results to perform additional operations. I perform a Steady State thermal analysis. No electric field time variation is considered. I find the Electric conductivity analogous thermal conductivity. Electric potential V is analogous to the temperature field. J (Current Density) is analogous to the Flux W/m2 Now I’m requesting -gradient (T) which is analogous to the electric Field E [V/m] With the dot product of J and E we could obtain the Joule power density distribution (W/m3). Nodal values. Formula Jx_Ex+Jy_Ey+Jz\*Ez. That Power density field is directly the input for a Body Flux [W/m3] in a regular thermal analysis Maybe Prepomax is not the most suitable for that kind of analisys. I see we would face another issue. Jx_Ex+Jy_Ey+Jz\*Ez ( W/m3) will give the Power density nodal values and in Prepomax Body Flux is based on Elements. I know one can import a temperature field form a txt file but ¿Could we import a Power density field [W/m3] based on nodes too.? I was just loking for workarrounds to a problem that shows up from time to time. ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 10:14am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/6 "2025-05-19T10:14:28Z")
Here’s an example of electrostatic analysis based on Elmer GUI tutorial - two charges with opposite signs are defined and temperature corresponds to potential. ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/7/7d7c690693c33e535e2fe01c59650434aeb6136a.png) [Electrostatics - two charges.pmx](https://prepomax.discourse.group/uploads/short-url/x3ab4TsqsNhQBEOHTV3UK4wxgnp.pmx) (4.7 MB) ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 10:44am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/7 "2025-05-19T10:44:41Z")
Nice!!. If we had available the Gradient of T , we could see the Electric Field and could compute Heat Flux \* Gradient(T) = Joule power density (W/m3) disipated inside the body. Another example: This is the Voltage drop inside a 2mm and 1mm lenght wire under a current of 20A. Directly computed inside Prepomax. For this simple case I can compute the Gradient of T and impose it to the same model beside as body flux to compute the thermal effect. ![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/9/98f5b05db1d6c00393ef0b54c4356b01cc954bf2.png) Final temperature at the surface is in excellent agreement with theory. (57.97ºC against Expected 58ºC) (I know It’s a very simple case but it shows prepomax could solve this problem with Steady State Thermal). Fully done inside Prepomax. One can see the analogy of results. In one case (Left) it should be read as Voltage (0.0002V) and the second (Right) it is final surface temperature. ![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/1/1347f5df5d54f8c8ee5ade08ceffa3cac5c1bb11.jpeg) ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 10:56am UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/8 "2025-05-19T10:56:39Z")
For Joule heating, I think I would use the \*ELECTROMAGNETICS step where you can prescribe voltage and current. There are some issues with it though: [Joule heating analysis - no degrees of freedom in the model - CalculiX (official versions are on www.calculix.de, the official GitHub repository is at https://github.com/Dhondtguido/CalculiX).](https://calculix.discourse.group/t/joule-heating-analysis-no-degrees-of-freedom-in-the-model/1141) ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 12:07pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/9 "2025-05-19T12:07:56Z")
I can’t open your file . ![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/2/269f15c246e4857974b71153737ea9e90b3159e5.png) ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 12:11pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/10 "2025-05-19T12:11:51Z")
I made it in v2.3.0. ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 12:21pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/11 "2025-05-19T12:21:00Z")
![imagen](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/e/e0c085fc7fab4ced953e2bcaf600435919b33e34.png) ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 12:23pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/12 "2025-05-19T12:23:19Z")
Strange, I can open it normally after downloading. Maybe try with this one: [Electrostatics v2.pmx](https://prepomax.discourse.group/uploads/short-url/qxr47Jy2GjzxNpVcCGQB4tTvxEb.pmx) (2.2 MB) ---
**Author:** ![belov](https://avatars.discourse-cdn.com/v4/letter/b/bc8723/32.png) [@belov](https://prepomax.discourse.group/u/belov)\ **Post date:** [May 19, 2025, 12:25pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/13 "2025-05-19T12:25:33Z")
![ElKin](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/1/1a56c53b546589890d33a0967109107c93632995.jpeg) ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 1:08pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/14 "2025-05-19T13:08:21Z")
@FEAnalyst Now it opens and I can see your spheres are in Air. Joule effect doesn’t have much sense here but the comments are valid anyway. @belov Thanks for the theoretical framework abstract. I should have started there to make me more understandable. I’m not considering magnetic fields at all. ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 1:11pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/15 "2025-05-19T13:11:59Z")
> [@ANYS](#): > > Now it opens and I can see your spheres are in Air. Joule effect doesn’t have much sense here but the comments are valid anyway. Yes, this was meant as regular electrostatics. I have another example for Joule heating (involving static current conduction) but it’s not working with CalculiX so far. ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 2:45pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/16 "2025-05-19T14:45:16Z")
@belov Is this problem stated at some book with their dimensions? I can’t find it. Looks very interesting as its not much complex and it has analytical solution. > [@FEAnalyst](#): > > I have another example for Joule heating (involving static current conduction ¿Could I take a look?. This Electro problems are new to me and would be nice to have more solved examples. ---
**Author:** ![belov](https://avatars.discourse-cdn.com/v4/letter/b/bc8723/32.png) [@belov](https://prepomax.discourse.group/u/belov)\ **Post date:** [May 19, 2025, 3:00pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/17 "2025-05-19T15:00:28Z")
Source: Manfred Filtz, Heino Henke.Ubungsbuch Elektromagnetischer Felder. Berlin: Springer Berlin Heidelberg, 2007 ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/7/71cd0d1aeb36e77152529032446d9f7550f574ff.png) ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/7/7392fa20242f239fd7acfb944abd28005326a3e1.png) ---
**Author:** ![FEAnalyst](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/feanalyst/32/688_2.png) [@FEAnalyst](https://prepomax.discourse.group/u/FEAnalyst)\ **Post date:** [May 19, 2025, 3:02pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/18 "2025-05-19T15:02:38Z")
> [@ANYS](#): > > Is this problem stated at some book with their dimensions? > I can’t find it. Looks very interesting as its not much complex and it has analytical solution. I’ve found it here: [https://youtu.be/Z\_vBsr6mDjw?si=HolxvyEMUz7tOLAT](https://youtu.be/Z_vBsr6mDjw?si=HolxvyEMUz7tOLAT) > [@ANYS](#): > > ¿Could I take a look?. This Electro problems are new to me and would be nice to have more solved examples. It’s implemented as built-in FEM example in FreeCAD 1.1.0 (named “Joule heating”). I don’t have a document for it yet. ---
**Author:** ![belov](https://avatars.discourse-cdn.com/v4/letter/b/bc8723/32.png) [@belov](https://prepomax.discourse.group/u/belov)\ **Post date:** [May 19, 2025, 3:04pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/19 "2025-05-19T15:04:25Z")
[Arcing horns protect bushings in case of the overvoltage.](https://quickfield.com/advanced/arcing_horns.htm) ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/e/e789bf84447e5bea59c5cb2fbf213fd519e0d313.png) ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/5/550ab4b9a63449dc29aef844371bfecedb9291fb.png) ![image](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/4/407e6607a3bebb5cfc9c1d82c2e6f8b84b6c6516.png) ---
**Author:** ![ANYS](https://yyz2.discourse-cdn.com/free1/user_avatar/prepomax.discourse.group/anys/32/7737_2.png) [@ANYS](https://prepomax.discourse.group/u/ANYS)\ **Post date:** [May 19, 2025, 7:44pm UTC](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712/20 "2025-05-19T19:44:47Z")
Good results. 😅 ![screenshot.74](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/7/722702ce831daffd6609d0dc60aa1672baad8d60.jpeg) ![screenshot.73](https://global.discourse-cdn.com/free1/uploads/prepomax/original/2X/3/3f77c683ce4b0824a2c1681fb65898caa8e0cb18.jpeg) Expected: RTOT 1.082E-05 Ohms Deviation 1.1% Thanks Again. EDITED: In case someone want’s to try I found that same problem as tutorial. [Electrokinetic Simulation Tutorials](https://magnetics.de/downloads/Tutorials/tutorials-electromagnetic-basic/7-electrokinetic-simulation-tutorials.html#circular-plate) [Next page](https://prepomax.discourse.group/t/electrostatics-electrokinetics-and-joule-effect/2712.md?page=2)