$A$ long solenoid has a radius $a$ and the number of turns per unit length is $n$. If it carries a current $i$,then the magnetic field on its axis is directly proportional to

$A$ steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement$(s)$ is (are) :
$(A)$ In the region $0 < r < R$,the magnetic field is non-zero.
$(B)$ In the region $R < r < 2R$,the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2R$,the magnetic field is tangential to the circle of radius $r$,centered on the axis.
$(D)$ In the region $r > 2R$,the magnetic field is non-zero.

$A$ solenoid $60 \;cm$ long and of radius $4.0\; cm$ has $3$ layers of windings of $300$ turns each. $A$ $2.0 \;cm$ long wire of mass $2.5\; g$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6.0\; A$ in the wire. What value of current (in $A$) in the windings of the solenoid can support the weight of the wire? $(g=9.8\; m \,s ^{-2})$

An infinitely long cylindrical wire of radius $a$ carries a steady current $I$ uniformly distributed across its cross-section. Determine the magnetic field $B$ at a distance $r$ from the axis for: $(a) r > a$,$(b) r = a$,$(c) r < a$,and $(d)$ at the axis $(r = 0)$.

$A$ current $i$ $A$ flows along an infinitely long straight thin-walled tube. The magnetic induction at any point inside the tube is:

What are the directions of the magnetic field between and outside a pair of two parallel large sheets carrying currents in the same directions,as illustrated in the figure?