Question

Find the electric field a distance z above the center of the square loop side a carrying uniform linee charges

Answer 1

The simplest method is to chop the line into symmetrically placed pairs (at ±x), quote the result of Ex. 2.1 (with d/2 → x, q → λ dx), and integrate (x : 0 → L).But here’s a more general approach:

For points far from the line (z >>L),

This makes sense: From far away the line looks like a point charge q = 2λL. In the limit L →∞, on the other hand, we obtain the field of an infinite straight wire:

E=

$2y \div z$

$1 \sqrt{4a eo}$