$A$ coil having $9$ turns carrying current $I$ produces a magnetic field $B_1$ at the centre. If the same wire is rewound into a coil of $3$ turns carrying the same current $I$,then the magnetic field at the centre $B_2$ is:

$A$ coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. When a current $i$ passes through the coil,the magnetic field at the centre is

The magnetic field at the centre $O$ of a square loop of side $a$ carrying current $I$ as shown in the figure is:

The figure shows the cross-section of a long cylindrical conductor through which an axial hole of radius $r$ is drilled with its centre at point $A$. $O$ is the centre of the conductor. If an identical hole were to be drilled centred at point $B$ while maintaining the same current density,the magnitude of the magnetic field at $O$:

As shown in the figure,two infinitely long,identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis,while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$,the magnitude of the magnetic field at $O$ is $10^{-4}\, T$,and the two wires carry equal current $i$ (see figure),find the magnitude of the current in each wire and the direction of the magnetic field at $O$. $(\mu_0 = 4\pi \times 10^{-7}\, NA^{-2})$

The figure shows a straight wire of length $l$ carrying current $i$. The magnitude of the magnetic field produced by the current at point $P$ is: