Question

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 centre 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 +j direction. Which of the following statements regarding the magnetic field vector B is (are) true? 

(A) If I₁ =I₂, then vector B cannot be equal to zero at the origin (0, 0, 0) 

(B) If I₁ > 0, and I₂ < 0, then vector B can be equal to zero at the origin (0, 0, 0) 

(C) If I₁ < 0, and I₂ > 0, then vector B can be equal to zero at the origin (0, 0, 0) 

(D) If I₁ = I₂, then the z-component of the magnetic field at the centre of the loop is (- μ₀I/2R)

Answer 1

solution (A, B, D)

(A) If I₁ = I₂, magnetic field due to infinite wires is equal to zero . So there must be a non–zero magnetic field at O due to the current carrying loop. 

(B) If I₁ > 0 & I₂ < 0 , magnetic field due to straight lines are along positive z–axis and due to loop it is along negative z–axis. 

(C) If I₁ < 0 & I₂ > 0 magnetic field due to straight wires are along negative z–axis and due to the loop it is also along negative z–axis