.......$A$ should be the current in a circular coil of radius $5\,cm$ to annul ${B_H} = 5 \times {10^{ - 5}}\,T$

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

If wire of length $L$ form a loop of radius $R$ and have $n$ turn. Find magnetic field at centre of loop if current flowing in loop is $I$

A straight wire of diameter $0.5\, mm$ carrying a current of $1\, A$ is replaced by another wire of $1\, mm$ diameter carrying the same current. The strength of magnetic field far away is

Magnetic field at the centre $O$ of a square loop of side $'a'$ carrying current $I$ as shown in the figure is

$AB$ and $CD$ are long straight conductor, distance $d$ apart, carrying a current $I$. The magnetic field at the midpoint of $BC$ is