The magnetic induction due to an ideal solenoid is independent of

What is an Amperian loop?

$A$ long solenoid with $ 40 $ turns per cm carries a current of $ 1 \,A $. The magnetic energy stored per unit volume is $ J m^{-3} $. (in $\pi$)

$A$ long solenoid carrying current $I_1$ produces a magnetic field $B_1$ along its axis. If the current is reduced to $20 \%$ and the number of turns per $cm$ is increased five times,then the new magnetic field $B_2$ is equal to:

Two long conductors are arranged as shown above to form overlapping cylinders,each of radius $r$,whose centers are separated by a distance $d$. Current of density $J$ flows into the plane of the page along the shaded part of one conductor and an equal current flows out of the plane of the page along the shaded portion of the other,as shown. What are the magnitude and direction of the magnetic field at point $A$?

$A$ $50 \ cm$ long solenoid has a winding of $400$ turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \ T$ at the centre (in $A$)?