Consider a uniformly charged circular loop and a uniformly charged straight wire. These two charge distributions create very different electric fields in the empty space that surrounds them. Even so, the divergence a distance $r$ from the center of the loop along its axis and the divergence the same distance $r$ from the wire's center have the same numerical value.

Question

Quizplus · Accepted Answer

The divergence of the electric field is proportional to the charge density. The charge density is the same for the loop and the wire at a distance $r$ from their centers. Therefore, the divergence of the electric field is the same for the loop and the wire at a distance $r$ from their centers.

Consider a Uniformly Charged Circular Loop and a Uniformly Charged rrr

Consider a Uniformly Charged Circular Loop and a Uniformly Charged $r$