$1)$Magnetic moment is a motion constant $(\backslash (\backslash$mathrm$\{$d$\}\backslash$mu $/\backslash$mathrm$\{$dt$\}=0\backslash ),$ for proof see the text books$).$ Exploiting this property, and constant kinetic energy of a particle in magnetic field only; find an equation relating the temporal change in magnetic field to the temporal change in parallel velocity component

$2)$Integrate this equation between two arbitrary points on a field line. Find a relation for the magnetic moment in terms of the parallel velocities and the magnetic field strength at these two points