1. The problem statement, all variables and given/known data Electrical force on a small positive charge q when it is placed in an electric field is given by F(r) = qE(r). Electric field is tangent at every point on a line of force. An analytical expression to plot electric field lines is given by E x dl = 0 Derive the following simplified analytical expression for electric field lines in, Cartesian, Cylindrical and Spherical coordinate systems dx/Ex = dy/Ey = dz/Ez 2. Relevant equations A X B = 0 , Parallel 3. The attempt at a solution If you equate Ex = dx , Ey= dy, Ez=dz the cross products for all coordinate systems will = 0 . However I really do not feel I have a clear grasp of what I am asked to show here. There is a chapter in our book "Engineering Electromagnetics" where plotting field lines it equates E to a differential length to plot the field lines, this is where I figured I could do this. Also F(r) = q E(r) and F is in the direction of E. Thoughts?