At what distance on the axis, from the centre of a circular current carrying coil of radius $r$, the magnetic field becomes $1 / 8$ th of the magnetic field at centre?

Two concentric circular loops, one of radius $R$ and the other of radius $2 R$, lie in the $x y$-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction, with $I_2>2 I_1 . \vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $x y$-plane. Which of the following statement($s$) is(are) current?

$(A)$ $\vec{B}(x, y)$ is perpendicular to the $x y$-plane at any point in the plane

$(B)$ $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r=\sqrt{x^2+y^2}$

$(C)$ $|\vec{B}(x, y)|$ is non-zero at all points for $r$

$(D)$ $\vec{B}(x, y)$ points normally outward from the $x y$-plane for all the points between the two loops

A coil of $12$ turns made by a constant length current carrying wire. If number of turns makes $3$ then change in magnetic field produced at its centre

A current $I$ flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is

In the given figure net magnetic field at $O$ will be

Find the magnetic field at $P$ due to the arrangement shown