The value of aluminium susceptibility is $2.2\times {10}^{-5}$. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $\frac{n}{{10}^4}$. Then the value of $n$ is

Figure $A$ and $B$ shown two long straight wires of circular cross-section ( $a$ and $b$ with $a<b$ ), carrying current $I$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $B$ varies with radius $r$ and can be represented as:

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 hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ?

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).