A Simple Method to Determine Electric and Magnetic Field Line Equations Using Flux Analysis

In this research, we provide a simple way to determine the equations of magnetic and electric field lines in any point using flux analysis. We believe that this technique will be understandable for undergraduate students because the required mathematical skill is quite simple. Moreover, this is also much simpler compared to the usual methods involving complex analysis or integration of the first-order differential equation of the field lines. In this method, we just need to know the vector field generated by the source and find the flux passing through a surface using basic calculus. We calculate the flux which goes through a surface and equate it with another surface having the same flux which is regarded as a constant. Therefore, we obtain the relation between the coordinates [Formula: see text] and [Formula: see text] in a single equation. We give several examples of the cases in electrostatics and magnetostatics as demonstrations.