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 centre, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I₂ is the clockwise direction, with ${\mathrm{I}}_2>2{\mathrm{I}}_1\cdot \overrightarrow{\mathrm{B}}(\mathrm{x},\mathrm{y})$ denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

${\mathrm{B}}_{\text{center }}=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_1}{2\mathrm{R}}\odot \frac{{\mathrm{\mu }}_0{\mathrm{i}}_2}{4\mathrm{R}}\otimes ,{\mathrm{i}}_2>2{\mathrm{i}}_1{\mathrm{SoB}}_{\text{center }}\mathrm{is}\otimes$

direction A $\overrightarrow{\mathrm{B}}$changes as we cross any wire

Due to radial symmetry B depends only on r.

consider point A just inside inner loop and B just outside it field at A due to inner loop is outward so there must be a null point somewhere between O&A (for r < R) Also field between the loops is in ward field just outside the outer loop is outward and at far a was points it is inwards. So there is another null point outside the outer loop two (for r > 2R)