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 +ĵ direction. Which of the following statements regarding the magnetic field B⃗ is (are) true ?
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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 +ĵ direction. Which of the following statements regarding the magnetic field B⃗ is (are) true ?

Select all that apply

G1 Physics · Accepted Answer

Add the fields of the two long wires and the circular loop vectorially at the origin and at the loop centre. Symmetry for I₁=I₂ prevents cancellation at the origin and yields loop-centre z-component −μ₀I/(2R). With I₁>0, I₂<0 the wire field can oppose the loop field and cancel it, whereas the opposite-sign arrangement in C cannot. Hence A,B,D.