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 $O$:

Two concentric coplanar circular loops of radii $r_1$ and $r_2$ carry currents of respectively $i_1$ and $i_2$ in opposite directions (one clockwise and the other anticlockwise). The magnetic induction at the centre of the loops is half that due to $i_1$ alone at the centre. If $r_2 = 2r_1$,the value of $i_2/i_1$ is:

$A$ charge $q$ $C$ moves in a circle at $n$ revolutions per second and the radius of the circle is $r$ $m$. The magnetic field at the centre of the circle is:

Two infinitely long thin wires are placed at $(1 \text{ cm}, 0 \text{ cm})$ and $(2 \text{ cm}, 0 \text{ cm})$ as shown in the figure. The same current $i$ flows in both the wires in the same direction, into the page. Let the magnetic field at the origin due to these wires be $\vec{B}$. If $B_0$ is the magnitude of the magnetic field if only the wire at $(1 \text{ cm}, 0 \text{ cm})$ was present, then the value of $B / B_0$ is

Which scientist established that electricity and magnetism are interrelated?

Two long parallel wires $X$ and $Y$,separated by a distance of $6 \text{ cm}$,carry currents of $5 \text{ A}$ and $4 \text{ A}$,respectively,in opposite directions as shown in the figure. The magnitude of the resultant magnetic field at point $P$,which is at a distance of $4 \text{ cm}$ from wire $Y$,is $x \times 10^{-5} \text{ T}$. The value of $x$ is . . . . . . .
Take the permeability of free space as $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$.