Ampere's law is true for which type of current?

In a toroid,the number of turns per unit length is $1000$ and the current through it is $\frac{1}{4 \pi} \ A$. The magnetic field produced inside (in $Wb/m^2$) will be:

$A$ long cylindrical wire of radius $R$ carries a uniform current $I$ flowing through it. The variation of magnetic field $B$ with distance $r$ from the axis of the wire is shown by:

$A$ long thin hollow metallic cylinder of radius $R$ carries a current $i$ ampere. The magnetic induction $B$ at a distance $r$ from the axis varies as shown in:

Consider two idealized systems: $(i)$ a parallel plate capacitor with large plates and small separation,and $(ii)$ a long solenoid of length $L \gg R$,where $R$ is the radius of the cross-section. In $(i)$,$E$ is ideally treated as a constant between the plates and zero outside. In $(ii)$,the magnetic field is constant inside the solenoid and zero outside. These idealized assumptions,however,contradict fundamental laws as follows:

$A$ current $I$ flows along the length of an infinitely long,straight,thin-walled pipe. Then: