Let the current $I$ be associated with an electron of charge $e$ moving in a circular orbit of radius $r$ with speed $v$ around the positively charged nucleus. The ratio $\frac{r}{v}$ is

$A$ long wire carries a steady current. It is bent into a coil of one turn such that the magnetic induction at the centre is $B$. If the same wire is bent to form a coil of smaller radius with $n$ turns,then the new magnetic induction $B^{\prime}$ at the centre is:

$A$ current $I$ flows in a wire bent in the shape of a quarter ring of radius $R$ as shown in the figure. The magnetic field induction $B$ at point $O$ is

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.

$A$ vertical wire kept in the $Z-X$ plane carries a current from $Q$ to $P$ (see figure). The magnetic field due to the current will have the direction at the origin $O$ along

$A$ single current-carrying loop of wire with current $I$ flowing in an anticlockwise direction when seen from the $+ve\;z$ direction,lying in the $xy$ plane,is shown in the figure. The plot of the $\hat{j}$ component of the magnetic field $(B_y)$ at a distance $a$ (less than the radius of the coil) on the $yz$ plane versus the $z$ coordinate looks like: