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- TL;DR Summary
- I would like to find an equation for E-field potentiality lines

Hi,

I am interested in finding the equation for electric field equipotential lines. Ideally, it would be nice to have one equation that worked to find it for different geometries. Unfortunately, I don't think that exists. Assuming it does not exist, I think I would probably have to either solve for the electric field intensity at a certain point...or arbitrarily pick a value that I know exists (using Maxwell's equations?). Assuming I'm in 2D, I would then pick a different X (or Y) and set the equation equal to the previous defined electric field intensity. I would do this for a lot of different X,Y combinations and start to see a line. Is this correct? If so, would I then have to plot those points and just use something like Matlab's curve fitting function to find the equation? Or how would I approach this?

I am interested in finding the equation for electric field equipotential lines. Ideally, it would be nice to have one equation that worked to find it for different geometries. Unfortunately, I don't think that exists. Assuming it does not exist, I think I would probably have to either solve for the electric field intensity at a certain point...or arbitrarily pick a value that I know exists (using Maxwell's equations?). Assuming I'm in 2D, I would then pick a different X (or Y) and set the equation equal to the previous defined electric field intensity. I would do this for a lot of different X,Y combinations and start to see a line. Is this correct? If so, would I then have to plot those points and just use something like Matlab's curve fitting function to find the equation? Or how would I approach this?