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

A
If I1=I2, then B cannot be equal to zero at the origin (0,0,0)
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B
If I1>0 and I2<0, then B can be equal to zero at the origin (0,0,0)
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C
If I1<0 and I2>0, then B can be equal to zero at the origin (0,0,0)
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D
If I1=I2, then the z-component of the magnetic field at the centre of the loop is (μ0I2R)
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Solution

## The correct options are A If I1=I2, then →B cannot be equal to zero at the origin (0,0,0) C If I1>0 and I2<0, then →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 (−μ0I2R)(A) At origin, →B=0 due to two wires if I1=I2 (they cancel each other) hence (→Bnet) at origin is equal to →B due to ring, which is non-zero. (B) If I1>0 and I2<0,→B at origin due to wires will be along +^k direction and →B due to ring is along −^k direction and hence →B can be zero at origin. (C) If I1<0 and I2>0,→B at origin due to wires is along −^k and also along −^k due to ring, hence →B cannot be zero. (D) (ref. image 2) At centre of ring, →B due to wires is along x-axis,hence z-component is only because of ring which →B=μ0I2R(−^K)

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