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  $I_2>2I_1.\overrightarrow{B}\left(x,y\right)$ denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

As per Biot – savart’s law, $d\overrightarrow{B}=\frac{{\mu }_0\overrightarrow{id\mathcal{l}}\times \overrightarrow{r}}{4\pi r^3}$

i.e., $\overrightarrow{B}$  is perpendicular to both $\overrightarrow{id\mathcal{l}}and\overrightarrow{r}$

$\overrightarrow{d\mathcal{l}}$ is in xy plane and $\overrightarrow{r}$ is also in xy plane

$\therefore d\overrightarrow{B}$ is perpendicular to xy plane 

Due to symmetry it depends only on distance from centre, 

radial distance $r=\sqrt{x^2+y^2}$

At centre $B_1=\frac{{\mu }_0{I}_1}{2R}and{B}_2=\frac{{\mu }_0{I}_2}{4R}clearly,B_2>B_1$

As we approach towards first loop $B_1$ increases to infinity hence $B_1$ dominates.

So it would be zero at some point between inner loops and centre.

Field will be in opposite direction inside and outside the loop