Electric Field Line Diagrams Don't Work
Electric Field Line Diagrams Don't Work, Am. J. Phys, 64(6) , June 1996.
Below, an example from the paper: 3 point charges of magnitude +1, +3,
and -4. Notice the bizarre clumping of electric field lines arriving at the
negative charge. The field lines are computed correctly, but this can't be
a proper representation of the electric field, because the field very close
to the -4 charge is nearly infinite, and therefore mostly due to that charge,
hence the electric field must be uniform. The conclusion is that 2-D field
lines patterns fail to correctly represent inherently 3-D electric fields.