The magnetic intensity at the centre of a long current-carrying solenoid is found to be $1.6 \times 10^3 \text{ A m}^{-1}$. If the number of turns is $8 \text{ per cm}$,then the current flowing through the solenoid is $................\, \text{A}$.

There is a long cylindrical pipe wire of internal radius $r$ and external radius $R$ carrying current $i$ along its length. The variation of magnetic field with distance from the axis of the wire can be represented by the :-

Give the formula for the magnetic field due to a toroid.

$A$ 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.

To manufacture a solenoid of length $\ell$ and inductance $L$,the length of the thin wire required is (Diameter of the solenoid is very small compared to its length,$\mu_0$ is the permeability of free space).

What is the magnetic field at point $P$ in the given figure?