The magnetic energy stored in a long solenoid of area of cross-section $A$ in a small region of length $L$ is

$A$ solenoid of length $50 \ cm$ and radius $10 \ cm$ has two closely wound layers of windings,each with $100$ turns. If a current of $2.5 \ A$ is passing through the windings,the magnetic field (in $10^{-4} \ T$) at a point $5 \ cm$ from the axis is:

$A$ solenoid is $1.0 \ m$ long and it has $4250$ turns. If a current of $5.0 \ A$ is flowing through it, what is the magnetic field at its centre? $[\mu_0 = 4\pi \times 10^{-7} \ T \cdot m/A]$

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:

$A$ current of $1/4\pi \ A$ is flowing through a toroid. It has $1000$ turns per meter. The value of the magnetic field (in $Wb/m^2$) along its axis is: