A $\backslash (20-\backslash$mathrm$\{$cm$\}\backslash )$ long solenoid consists of $100$ turns of a coil of radius $\backslash ($ r$=3\mathrm{.}0\backslash$mathrm$\{$~cm$\}\backslash ).$ A current of $\backslash ($ I$\_\{0\}\backslash )$ in the coiled wire produces a magnetic field of $\backslash ($ B$\_\{0\}\backslash )$ in the middle of the solenoid. If we wish to produce a field that is $4-$times larger, which of the following changes could work?

i$)$ cut the radius of the coil to one$-$half

ii$)$ quadruple the number of turns in the $\backslash (20-\backslash$mathrm$\{$cm$\}\backslash )$ long solenoid

iii$)$ half the length of the $100-$turn solenoid but maintain $100$ turns across that length.

iv$)$ quadruple the length of the $100-$turn solenoid, but also double the radius of the coil.

v$)$ half the length of the solenoid, and double the number of turns to $200$ total turns

vi$)$ double the current in the wire, and double the number of turns in the $\backslash (20-\backslash$mathrm$\{$cm$\}\backslash )$ long solenoid