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 :-

$A$ solenoid has a length of $0.4 \,m$, a radius of $1 \,cm$, and $400$ turns of wire. If a current of $5 \,A$ is passed through this solenoid, what is the magnetic field inside the solenoid?

If the magnetic field inside a solenoid is $B$,then the magnetic energy stored in it per unit volume is (where $c$ is the speed of light in vacuum and $\varepsilon_0$ is the permittivity of free space).

$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of winding of $N$ turns each. If it carries a current $I$,the magnetic field at its centre will be

$A$ solenoid is $1.5 \, m$ long and its inner diameter is $4.0 \, cm$. It has three layers of windings of $1000$ turns each and carries a current of $2.0 \, A$. The magnetic flux for a cross-section of the solenoid is nearly:

$A$ magnetic field of $100 \;G$ $(1 \;G = 10^{-4} \;T)$ is required which is uniform in a region of linear dimension about $10 \;cm$ and area of cross-section about $10^{-3} \;m^2$. The maximum current-carrying capacity of a given coil of wire is $15 \;A$ and the number of turns per unit length that can be wound round a core is at most $1000 \;turns \;m^{-1}$. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.