The magnetic field intensity $H$ at the centre of a long solenoid having $n$ turns per unit length and carrying a current $I$,when no material is kept in it is ($\mu_0 =$ permeability of free space).

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{th}$,then the new value of the magnetic field will be:

$A$ toroid has an iron core with an internal magnetic field of $10 \pi \text{ mT}$,when the current in the winding of $1500 \text{ turns/m}$ is $10 \text{ A}$. Determine the field due to magnetization $(\mu_0 = 4 \pi \times 10^{-7} \text{ H m}^{-1})$.

$A$ solenoid has a core of a material with relative permeability $400$. The windings of the solenoid are insulated from the core and carry a current of $4 \,A$. If the number of turns is $500$ per metre,then the magnetizing field is

Verify Ampere's law for the magnetic field of a point dipole with dipole moment $\vec{M} = M\hat{k}$. Take $C$ as the closed curve running clockwise along the quarter circle of radius $R$ and center at the origin,in the first quadrant of the $x-z$ plane.

What is the magnetic field at point $P$ located at a distance of $\frac{3R}{2}$ from the center of the cylindrical conductor with inner radius $R$ and outer radius $2R$ carrying a current $i$?