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

There are $50$ turns of a wire in every $1$ $cm$ length of a long solenoid. If $4$ $A$ current is flowing in the solenoid,the approximate value of the magnetic field along its axis at an internal point and at one end will be respectively:

$A$ straight wire of diameter $0.4 \,mm$ carrying a current of $2 \,A$ is replaced by another wire of $0.8 \,mm$ diameter carrying the same current. The magnetic field at distance $R$ from both the wires is $B_1$ and $B_2$ respectively. The relation between $B_1$ and $B_2$ is

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

$A$ solenoid has a turn density of $5000 \, \text{turns/m}$ and a cross-sectional area of $10 \, \text{cm}^2$. If a current of $1 \, \text{A}$ flows through it and the core material has a relative permeability of $1000$, find the energy per unit length of the solenoid in $\text{J/m}$.

$A$ solenoid of length $2 \ m$ carries a current of $20 \ A$. The diameter of the solenoid is $3 \ cm$. If the magnetic field inside the solenoid is $20 \ mT$, then the length of wire forming the solenoid is (assume $\mu_0 = 4 \pi \times 10^{-7} \ H/m$) (in $m$)