A current-carrying circular loop and a current-carrying straight wire create very different magnetic fields in the empty space that surrounds them. Even so, the curl of $\vec{B}$ at a distance $r$ from the center of the loop along its axis and the magnitude of the curl the same distance $r$ from the wire's center have the same numerical value.

Question

Quizplus · Accepted Answer

The curl of $\vec{B}$ is proportional to the current density, which is the same for the loop and the wire at a given distance from their centers.

A Current-Carrying Circular Loop and a Current-Carrying Straight Wire Create B⃗\vec{B}B

A Current-Carrying Circular Loop and a Current-Carrying Straight Wire Create $\vec{B}$