As part of one of our research projects, one of my students has just acquired a set of tiny electrodes, set into plastic in a grid-like pattern. We'll use this array to measure the electrical conductivity of various fluids. We don't need 60 electrodes, about 4 would do nicely, but the particular company concerned makes the electrode arrays like this, so that's what we've got. My student asked the reasonable question of whether the presence of the unused electrodes would significantly change the electric fields set up by the 4 that we would be using - i.e. would it significantly affect our measurements of conductivity.
Well, a metal electrode, even one not connected to anything, isn't fluid, so yes, there would be some effect, but how big? Is it one we need to worry about? I suggested he use a piece of computer software we have to 'model' this situation - let the computer find what the electric fields look like with all the redundant electrodes present and see.
Easier said than done. Poor student devoted last Saturday to the task, which was unsuccessful. The software seems to be playing up. So I said that I'd have a good look at his work and see if I could work out what was going on. So yesterday morning, I basically pulled apart the computer model he had made and reconstructed it again, making sure everything was correct. And, bingo, the software ran, solved the problem, and gave me some lovely pictorial representations of the electric fields around these tiny electrodes.
Problem solved? Well, no. Because at this point I start applying my brain to the problem, and ask whether the solution (as pretty as it is) looks physically reasonable. What do I mean by that? Well, I know that electric field lines travel from high potential to low potential. They hit good conductors at normal incidence to the conductor. Where there is a field in a conductor, currents are going to flow. And so on. And looking carefully at the solution the computer gave me, I could see that in one aspect it didn't look right. All my extra electrodes seemed to have magically earthed themselves. Why? I have no idea. I've trawled through the model and can't find anywhere where I've told the computer that these things are earthed. I just don't know at the moment what's going on.
But, here is my point (at last, I hear you say). If I just assumed the output from the computer programme was 'right', I'd have been making a big mistake. A computer programme, no matter how much it costs, always has to be run in parallel with your brain. You've got to ask yourself whether the output looks physically reasonable before you go and do anything with it, especially things that could prove expensive if you get it wrong. I'm glad I took the time to do this, before giving my already overworked student duff results.