# When is the flux through a coil from a bar magnet zero?

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## Main Question or Discussion Point

Suppose I have a finite sized cylindrical bar magnet of radius $a$ and length $b$. It is coaxial with the $x$ axis and moving from $-\infty$ to $\infty.$ A circular closed wire of radius $r>a$ is in the $y-z$ plane with center at the origin. When the bar center of the bar magnet passes through the origin, what is the total flux through the wire?

The answer is not necessarily zero because note that by increasing the radius $r$ we can increase the total flux through the wire. So what does the flux as a function of the position of the center of mass of the bar magnet look like?