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.

$A$ long solenoid with $10.0 \text{ turns/cm}$ and a radius of $8 \text{ cm}$ carries a current of $7 \text{ mA}$. $A$ current-carrying straight conductor is located along the central axis of the solenoid. If the direction of the resulting magnetic field is $60^{\circ}$ to the axial direction at a point $5 \text{ cm}$ from the axis of the solenoid along the radial direction, then the current in the conductor is. [Take $\sqrt{2}=1.4, \sqrt{3}=1.7$] (in $\text{ A}$)

$A$ toroid has $500$ turns per metre length. If it carries a current of $2 \text{ A}$, the magnetic energy density inside the toroid is: (in $\text{ J/m}^3$)

$A$ 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

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:

$A$ toroidal solenoid with air core has an average radius $R$,number of turns $N$,and area of cross-section $A$. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid).