 #1
zenterix
 66
 20
 Homework Statement

While reading Chapter 1 of Purcell's Electricity and Magnetism, I noticed there are various paragraphs where he attempts to make an intuitive argument to explain a concept, result, or equation. Here is an example that I can't understand.
"The field of an infinitely long line charge, we found, varies inversely as the distance from the line, while the field of an infinite sheet has the same strength at all distances. These are simple consequences of the fact that the field of a point charge varies as the inverse square of the distance. If that doesn’t yet seem compellingly obvious, look at it this way: roughly speaking, the part of the line charge that is mainly responsible for the field at P in Fig. 1.24 is the near part – the charge within a distance of order of magnitude r. If we lump all this together and forget the rest, we have a concentrated charge of magnitude ##q \approx \lambda r##, which ought to produce a field proportional to ##\frac{q}{r^2}## or ##\frac{\lambda}{r}##. In the case of the sheet, the amount of charge that is “effective,” in this sense, increases proportionally to ##r^2## as we go out from the sheet, which just offsets the ##\frac{1}{r^2}## decrease in the field from any given element of charge.
 Relevant Equations

The confusing part for me starts at "roughly speaking".
The "near" part of the line: is that a point or a section of the line?
What are we "lumping" together exactly? ##\lambda r## seems like the charge that we'd have if the charge were distributed along the line from point ##P## to the line charge.