$A$ very long wire carrying a current $I = 4 \sqrt{2} \, A$ is bent at a right angle. The magnitude of the magnetic field $(|B|)$ at a point $P$ lying on a line perpendicular to the bent wire at a distance $d = 20 \, cm$ from the point of the bending will be (Let $\mu_0 = 4 \pi \times 10^{-7} \, H/m$): (in $\, \mu T$)

$A$ long solenoid with $1000 \, \text{turns/m}$ has a core material with relative permeability $500$ and volume $10^{3} \, \text{cm}^{3}$. If the core material is replaced by another material having relative permeability of $750$ with the same volume, maintaining the same current of $0.75 \, \text{A}$ 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 $x$.

$A$ current loop, having two circular arcs joined by two radial lines, is shown in the figure. It carries a current of $10 \, A$. The magnetic field at point $O$ will be close to:

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is:

The resistances of three parts of a circular loop are as shown in the figure. The magnetic field at the centre $O$ is:

Two identical circular current loops of radius $R$ carrying equal currents $I$ are placed such that their axes are inclined at $45^\circ$ to each other. The distance from the center of each loop to point $P$ is $\sqrt{3}R$. The resultant magnetic field at $P$ is: