THERE IS ENOUGH INFORMATION PROVIDED:

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 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 $3.$