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Using the Biot-Savart law, find the magnetic field at an arbitrary point on the $z$-axis of a circular loop or radius $a$ carrying a current $I$ counterclockwise around the $z$-axis and centered on the origin in the $x$-$y$ plane. Draw the arrangement in the space provided above, of course. Show all work - don't just write the answer down even. Then find the field in the limit that $z \gg a$ and show that it is the familiar field of a (magnetic) dipole on its axis.