How far away is infinity? An electromagnetics exercise to develop intuition regarding models

Abstract

The estimation of the electric field in simple situations provides an opportunity to develop intuition about the models used in physics. We propose an activity aimed at university students where the electric field of a finite line of charge is compared, analytically or numerically, with the fields of an infinite line and of a point charge. Contrary to intuition, it is not necessary to get very close for the line charge to be considered infinite, nor to move very far away for the finite line field to resemble that of a point charge. We conducted this activity with a group of students and found that many of them have not yet developed an adequate intuition about the approximations used in electromagnetism.