Two infinitely long straight wires lie in the $\mathrm{xy}$-plane along the lines $\mathrm{x}=+R$. The wire located at $\mathrm{x}=+\mathrm{R}$ carries a constant current $\mathrm{I}_1$ and the wire located at $\mathrm{x}=-R$ carries a constant current $\mathrm{I}_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the xy-plane. This loop carries a constant current $/$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{\mathrm{j}}$ direction. Which of the following statements regarding the magnetic field $\dot{B}$ is (are) true?
$(A)$ If $I_1=I_2$, then B' cannot be equal to zero at the origin $(0,0,0)$
$(B)$ If $\mathrm{I}_1>0$ and $\mathrm{I}_2<0$, then $\mathrm{B}$ can be equal to zero at the origin $(0,0,0)$
$(C)$ If $\mathrm{I}_1<0$ and $\mathrm{I}_2>0$, then $\mathrm{B}$ can be equal to zero at the origin $(0,0,0)$
$(D)$ If $\mathrm{I}_1=\mathrm{I}_2$, then the $\mathrm{z}$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}}\right)$
IIT 2018, Advanced
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