Two infinitely long straight wires lie in the $xy$-plane along the lines $x=+R$ and $x=-R$. 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 $xy$-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?
$(A)$ 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 $\left(-\frac{\mu_0 I}{2 R}\right)$.

• A
  $A, B, D$
• B
  $A, B$
• C
  $A, C$
• D
  $A, B, C$