The magnetic field $(B)$ inside a long solenoid having '$n$' turns per unit length and carrying current '$i$' when an iron core is kept in it,is ($\mu_0 =$ permeability of vacuum,$\chi =$ magnetic susceptibility).

What is a solenoid? And what is a long solenoid? Explain.

$A$ rod with a circular cross-section area of $2\,cm^2$ and a length of $40\,cm$ is wound uniformly with $400$ turns of an insulated wire. If a current of $0.4\,A$ flows in the wire windings,the total magnetic flux produced inside the windings is $4\pi \times 10^{-6}\,Wb$. The relative permeability of the rod is (Given: Permeability of vacuum $\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A$)

$A$ solenoid having area $A$ and length $l$ is filled with a material having relative permeability $2$. The magnetic energy stored in the solenoid is

The current in the windings of a toroid is $2.0\,A$. There are $400\,turns$ and the mean circumferential length is $40\,cm$. If the inside magnetic field is $1.0\,T$, the relative permeability is near to

$A$ cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. $A$ uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12} \mu_0 aJ$,then the value of $N$ is: