The free space inside a current-carrying toroid is filled with a material of magnetic susceptibility $2 \times 10^{-2}$. The percentage increase in the value of the magnetic field inside the toroid will be $.....\%$.

An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface. Choose the correct representation of magnetic field $(B)$ as a function of radial distance $(r)$ from the axis of the cylinder.

$A$ 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 $(\mu_0 = 4 \pi \times 10^{-7} \text{ H m}^{-1})$.

$A$ long solenoid produces a magnetic field $B$ on its axis. If it is cut into four equal parts and,for the same current,half the number of turns are wound on any one piece,the value of the magnetic field on its axis becomes:

$A$ closely wound solenoid $80\; cm$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8\; cm$. If the current carried is $8.0\; A$,estimate the magnitude of $B$ inside the solenoid near its centre.

$A$ solenoid has a core made of material with relative permeability $400$. The magnetic field produced in the interior of the solenoid is $1.0 \text{ T}$. The magnetic intensity in $SI$ units is $\alpha \times 10^5$. The value of $\alpha$ is . . . . . . . (Free space permeability $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.)