Electric Field Line Homework: Deriving Analytical Expressions

[Roy Fokker]

Homework Statement

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

Homework Equations

A X B = 0 , Parallel

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?

 

[deskswirl]

E x dl = 0 implies E and dl are colinear. So try writing dl as a scaled version of E. For instance, dl=wE where w is a scaling factor ensuring they have the same length. If you expand in vector components I think you'll find the necessary relation.

BTW, out of interest, which "Engineering Electromagnetics" book is this?