Two infinitely long straight wires lie in the xy-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 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 J` direction. Which of the following statements regarding the magnetic field ` vec B` is (are) true?

Options

A. If `I_(1)=I_(2)`, then `vecB` cannot be equal to zero at the origin (0,0,0)
B. If `I_(1)gt0` and `I_(2)lt0`, then `vecB` can be equal to zero at the origin (0,0,0)
C. If `I_(1)lt0andI_(2)gt0`, then `vecB` 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 `(-(mu_(0)I)/(2R))`

Answer

A, B, D