Two toroids with number of turns $400$ and $200$ have average radii $30 \ cm$ and $60 \ cm$ respectively. If they carry the same current,the ratio of magnetic fields in these two toroids is:

$A$ 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 $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.)

$A$ solenoid of length $0.5 \ m$ has a radius of $1 \ cm$ and is made up of $250$ turns. It carries a current of $5 \ A$. What is the magnitude of the magnetic field inside the solenoid?

$A$ long cylindrical conductor with a large cross-section carries an electric current distributed uniformly over its cross-section. The magnetic field due to this current is:

The magnetic field at the centre of a long solenoid having $400$ turns per unit length and carrying a current $i$ is $6.24 \times 10^{-2} \,T$. The magnetic field at the centre of another long solenoid having $200$ turns per unit length and carrying a current $\frac{i}{2}$ is

$A$ steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement$(s)$ is (are) :
$(A)$ In the region $0 < r < R$,the magnetic field is non-zero.
$(B)$ In the region $R < r < 2R$,the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2R$,the magnetic field is tangential to the circle of radius $r$,centered on the axis.
$(D)$ In the region $r > 2R$,the magnetic field is non-zero.