The resistances of three parts of a circular loop are as shown in the figure. The magnetic field at the centre $O$ is:

An infinitely long wire carrying $1 \ A$ current in the $+z$ direction is placed at $(1 \ cm, 1 \ cm)$. Another wire carrying $1 \ A$ in the $+x$ direction is placed at $y=1 \ cm$. If the magnetic field due to this configuration at the origin is $B$. Let $B_0$ be the magnitude of the field if only the wire at $(1 \ cm, 1 \ cm)$ was present,then $\frac{B}{B_0}$ is

In the previous question,if the current is $i$ and the magnetic field at $D$ has magnitude $B$,

Two concentric coils $X$ and $Y$ of radii $16 \, cm$ and $10 \, cm$ lie in the same vertical plane containing $N-S$ direction. Coil $X$ has $20$ turns and carries $16 \, A$. Coil $Y$ has $25$ turns and carries $18 \, A$. Coil $X$ has current in anticlockwise direction and coil $Y$ has current in clockwise direction for an observer looking at the coils facing the west. The magnitude of the net magnetic field at their common centre is:

The magnetic field induction produced at the centre of orbit due to an electron revolving in $n^{\text{th}}$ orbit of a hydrogen atom is proportional to

$A$ straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is