What is the formula for magnetic field for a long solenoid?

A long solenoid is formed by winding $70$ turns ${\mathrm{cm}}^{-1}$ . If $2.0 \mathrm{A}$ current flows, then the magnetic field produced inside the solenoid is ______________.

$({\mu }_0= 4\mathrm{\pi }\times {10}^{–7} \mathrm{T} \mathrm{m} {\mathrm{A}}^{–1})$

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

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\mathrm{\pi }}{10} m$ is carrying current $I = 3A$. The magnitude of the magnetic field. at the center $O$ of the arc is: (The permeability of the vacuum $= 4\mathrm{\pi }\times {10}^{-7}{\mathrm{NA}}^{-2}$ )

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

A rod with circular cross-section area $2 {\mathrm{cm}}^2$ and length $40 \mathrm{cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current of $0.4 \mathrm{A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4\mathrm{\pi }\times {10}^{-6} \mathrm{Wb}$. The relative permeability of the rod is

(Given : Permeability of vacuum ${\mathrm{\mu }}_0=4\mathrm{\pi }\times {10}^{-7} \mathrm{N} {\mathrm{A}}^{-2}$)

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).