An iron ring of relative permeability has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring. (b)Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

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

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).