$A$ 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:

$A$ hollow cylinder of infinite length carries a uniform current per unit length $\lambda$ along its circumference,as shown. The magnetic field inside the cylinder is:

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

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

Inductance per unit length near the middle of a long solenoid is ($\mu_0=$ permeability of free space,$n=$ number of turns per unit length,$d=$ the diameter of the solenoid).

$A$ solenoid has a core of a material with relative permeability of $400$. The solenoid windings are insulated from the core and carry a current of $2 \text{ A}$. If the number of turns is $1000$ per meter,then the value of magnetic intensity will be . . . . . . .