Solenoid S whose cross$-$section is shown in Fig. $3$ is wrapped with n turns of wire

per its unit length. It also contains a thin insulating circular loop L of radius r

that is coaxial with the solenoid. A small positively charged bead B $($given charge

q and mass m $)$ can slide without friction along this loop. As observed now, the

counterclockwise current feeding the solenoid wire equals to I$\_(1),$ while the bead

moves with speed u$=$u$\_(1)$ in the clockwise direction. Then the feeding current is

increased in some fashion to magnitude I$\_(2)>$ I$\_(1).$ Would the bead's speed change

as a result $($and why$)?$ If not, then state that u$\_(2)=$u$\_(1).$ Otherwise, find the "new"

speed u$\_(2)$ after the current becomes equal to I$\_(2).$ Given that the particle can move

$($that$\text{'}$s$,$ velocity$)$ in two opposite directions on the loop, we refer to speed here as

the magnitude of the velocity v:u$=|$v$|.$

Figure $3$: Illustration for problem $3.$

could you help me set this up