Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I₁ and the wire located at x = −R carries a constant current I₂. A circular loop of radius R is suspended with its center at (0, 0, √3R) 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 +ĵ direction. Which of the following statements regarding the magnetic field →B is (are) true?

The correct options are A, B, and D.

(A) At the origin, →B = 0 due to two wires if I₁ = I₂ (they cancel each other) hence (→Bnet) at the origin is equal to →B due to the ring, which is non-zero.

(B) If I₁ > 0 and I₂ < 0, →B at the origin due to wires will be along +k̂ direction and →B due to the ring is along −k̂ direction and hence →B can be zero at the origin.

(C) If I₁ < 0 and I₂ > 0, →B at the origin due to wires is along −k̂ and also along −k̂ due to the ring, hence →B cannot be zero.

(D) (ref. image 2) At the center of the ring, →B due to wires is along the x-axis, hence the z-component is only because of the ring which →B = μ₀I/2R(−k̂)