A solenoid is constructed by winding a wire of diameter $d$ around a cylinder of a fixed height $h$ and a fixed radius $r\left(h\gg r\gg d\right)$ such that a magnetic field of a fixed magnitude $B$ is produced along the axis of the cylinder when an appropriate current is passed through the wire. The winding must be tight, with negligible space left between adjacent turns, and there is only one layer of wire on the cylinder. Choose the correct statement(s).

Choose the correct statement in the following:

(a) The magnetic field inside the solenoid is greater than that of outside
(b) The magnetic field inside an ideal solenoid is not at all uniform
(c) The magnetic field at the centre, inside an ideal solenoid is almost twice that at the ends
(d) The magnetic field at the centre, inside an ideal solenoid is almost half of that at the ends

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).

A solenoid of length $50 \mathrm{cm}$, having $100 \mathrm{turns}$ carries a current of $2.5 \mathrm{A}$. Find the magnetic field, (a) in the interior of the solenoid, (b) at one end of the solenoid.  Given ${\mathrm{\mu }}_0=4\mathrm{\pi }\times {10}^{-7}{\mathrm{WbA}}^{-1}{\mathrm{m}}^{-1}$.

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$=4\pi \times {10}^{-7} \mathrm{H} {\mathrm{m}}^{-1}$)