$A$ long solenoid with $ 40 $ turns per cm carries a current of $ 1 \,A $. The magnetic energy stored per unit volume is $ J m^{-3} $. (in $\pi$)

$A$ toroid has a non-ferromagnetic core of inner radius $24 \ cm$ and outer radius $25 \ cm$,around which $4900$ turns of a wire are wound. If the current in the wire is $12 \ A$,the magnetic field inside the core of the toroid is: (in $mT$)

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field,$|\vec B |$ as a function of the radial distance $r$ from the axis is best represented by:

$A$ long solenoid is fabricated by closely winding a wire of radius $0.5 \, mm$ over a cylindrical frame so that the successive turns nearly touch each other. What is the magnetic field at the centre of the solenoid if it carries a current of $5 \, A$?

"On flowing current in a conducting wire, a magnetic field is produced around it." This is a law of

Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same, then the ratio of magnitude of magnetic fields of the two solenoids $\frac{|B_X|}{|B_Y|}$ is