A long cylindrical wire of radius $R$ carries a uniform current $I$ flowing through it. The variation of magnetic field with distance $\text{'}r\text{'}$ from the axis of the wire is shown by

A very long straight wire of radius $r$ carries current $I$. Intensity of magnetic field $B$ at a point lying at a perpendicular distance $a$ from the axis is $\propto$ _____ $(\text{where} a<r)$.

Two very long straight wires are set parallel to each other. Each carries a current $I$ in the same direction and the separation between them is $2r.$ The intensity of the magnetic field at point $P$ as shown in the figure is _________.

A toroidal coil has $3000$ turns. The inner and outer radii are $10 \mathrm{cm}$ and $12 \mathrm{cm}$, respectively. If current flowing is $5 \mathrm{A}$, then the magnetic field inside the toroid will be

A solenoid of $1000$ turns per metre has a core with relative permeability $500.$ Insulated windings of the solenoid carry an electric current of $5 \mathrm{A}.$ The magnetic flux density produced by the solenoid is:

(Permeability of free space$=4\pi \times {10}^{-7} \mathrm{H} {\mathrm{m}}^{-1}$)

Four identical long solenoids $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are connected to each other as shown in the figure. If the magnetic field at the center of $\mathrm{A}$ is $3 \mathrm{T}$ the field at the center of $\mathrm{C}$ would be : (Assume that the magnetic field is confined with in the volume of respective solenoid).