A magnetic dipole $m$ aligned in the $-z$ direction is moved from $z=$ towards

a perfectly conducting circular ring of radius $r$ and self$-$inductance $L($see diagram$).$

When the dipole is at $z=,$ there is no current in the ring.

$($a$)$ Find the field due to the dipole.

$($b$)$ Find the flux through the ring due to this field.

$($c$)$ Using Lenz's law, or otherwise, find the current in the ring when the dipole

arrives at its final location at distance $z$ from the ring.

$($d$)$ Find the force on the dipole at its final location shown in the figure.