The magnetic field at the center of a current-carrying circular loop is $B_{1}$. The magnetic field at a distance of $\sqrt{3}R$ from the center on its axis is $B_{2}$,where $R$ is the radius of the loop. The value of $B_{1} / B_{2}$ is:

$A$ thin ring of radius $R$ carries a uniformly distributed charge. The ring rotates at a constant speed $N$ r.p.s. about its axis perpendicular to the plane. If $B$ is the magnetic field at the centre,the charge on the ring is ($\mu_0 =$ permeability of free space).

Equal currents $I$ are flowing in three infinitely long wires along the positive $x$,$y$,and $z$ directions. The magnetic field at a point $(0, 0, -a)$ would be:

An electron revolves around a nucleus with rotational frequency $f$ in a circular orbit. Due to this,the magnetic induction produced at the nucleus position is $B$. The radius of the circular orbit is directly proportional to:

At what distance from a long straight wire carrying a current of $12 \, A$ will the magnetic field be equal to $3 \times 10^{-5} \, Wb/m^2$?

Two concentric circular loops,one of radius $R$ and the other of radius $2R$,lie in the $xy$-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 $I_2 > 2I_1$. $\vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $xy$-plane. Which of the following statement$(s)$ is(are) correct?
$(A)$ $\vec{B}(x, y)$ is perpendicular to the $xy$-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 $xy$-plane for all the points between the two loops.