Correct answer is (2)

In a solenoid, the magnetic field intensity ($H$) is given by the product of the number of turns per unit length ($n$) and the current ($I$) flowing through the solenoid. This can be represented mathematically as:

$H=nI$

This is actually derived from Ampere's law applied to the special case of a solenoid, where the magnetic field is uniform and directed along the axis of the solenoid.

If we rearrange this equation to solve for the current ($I$), we get:

$I=\frac{H}{n}$

In this problem, we're given that the magnetic field intensity ($H$) at the center of the solenoid is $1.6\times {10}^3{\text{Am}}^{-1}$ and the number of turns per unit length ($n$) is 8 per cm (which is equal to $8\times {10}^{-2}$ per meter, as there are 100 cm in a meter).

Substituting these values into the equation gives:

$I=\frac{1.6\times {10}^3{\text{Am}}^{-1}}{8\times {10}^{-2}\text{turns/m}}=2\text{A}$

So, the current flowing through the solenoid is $2\text{A}$.

Correct Option is (A)

$\overrightarrow{B^{\prime }}={\mu }_0(1+X)ni$ (in the material)

$\overrightarrow{B^{\prime }}={\mu }_{0}ni$ (without material)

So fractional increase is

$\frac{B^{\prime }-B}{B}=X=1.2\times {10}^{-5}$

Correct Option is ()

Correct Option is (A)

For diamagnetic material

$\chi$ is independent of temperature and negative.

Magnetisation (M) is directly proportional to H (The relation between magnetisation and magnetising field, M = –mH)

Option (a)

Correct Option is (B)

$\mu$ = $\mu$₀ (1 + x_m)

= 4$\pi$ $\times$ 10^$-$7 $\times$ 500

= 2$\pi$ $\times$ 10^$-$4 H/m