A current$-$carrying wire moves toward a coil

A long straight wire carrying current $\backslash ($ I $\backslash )$ is moving with speed $\backslash ($ v $\backslash )$ toward a small circular coil of radius $\backslash ($ r $\backslash )$ containing $\backslash ($ N $\backslash )$ turns, which is attached to a voltmeter as shown. The long wire is in the plane of the coil. $($Only a small portion of the wire is shown in the diagram.$)$

The radius of the coil is $0\mathrm{.}02$ m $,$ and the coil has $11$ turns. At a particular instant $\backslash ($ I$=4\backslash )$ amperes, $\backslash ($ v$=2\mathrm{.}9\backslash )$ meters per second, and the distance from the wire to the center of the coil $\backslash ($ x$=0\mathrm{.}17\backslash$mathrm$\{$~m$\}\backslash ).$

Part $1$

$*$ Your answer is incorrect.

$($a$)$ What is the magnitude of the rate of change of the magnetic field inside the coil? You will need to derive a formula using calculus before you can get a number. Begin with the expression for the magnetic field due to the wire at the location of the coil. Use the approximate formula, since the wire is very long. Remember the chain rule, and remember that $\backslash ($ v$=\backslash$frac$\{$d x$\}\{$d t$\}\backslash ).$

$\backslash [$

$\backslash$frac$\{$d B$\}\{$d t$\}=$

$\backslash ]$

Attempts: $1$ of $10$ used

Part $2$

$($b$)$ What is the magnitude of the voltmeter reading? Remember that this includes all $11$ turns of the coil.