A long solenoid with $1000 \mathrm{turns} {\mathrm{m}}^{-1}$ has a core material with relative permeability $500$ and volume ${10}^3{ \mathrm{cm}}^3.$ If the core material is replaced by another material having relative permeability of $750$ with same volume maintaining same current of $0.75 \mathrm{A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right).$ Find the value of $x.$

Following plots show Magnetization $\left(M\right)$ vs Magnetising field $\left(H\right)$ and Magnetic susceptibility $\left(\mathrm{\chi }\right)$ vs Temperature $\left(T\right)$ graph :

Which of the following combination will be represented by a diamagnetic material?

There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is $1:1$. The magnetic field at point $P$ is$\_\_\_\_\_\_\_\_\_.$

Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet.

Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below: