Two infinitely long straight wires lie in the $x y$-plane along the lines $x= \pm R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the $x y$-plane. This loop carries a constant current $I$ 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 $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\vec{B}$ is (are) true?
Select ALL correct options:
A
If $I_1=I_2$, then $\vec{B}$ cannot be equal to zero at the origin $(0,0,0)$
B
If $I_1>0$, and $I_2<0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$
C
If $I_1<0$, and $I_2>0$, then $\vec{B}$ can be equal to zero at the origin $(0,0,0)$
D
If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 I}{2 R}\right)$
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