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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 option is D If I1=I2, then the z-component of the magnetic field at the centre of the loop is (−μ0I2R) For option A: if I1=I2 then the magnetic field due to infinite wire will be equal to zero. Hence no non-magnetic field will produce on behalf of current carring loop. Hence, option A is correct. For option B: If i1>0 and i2<0 then the magnetic field due to straght line will be in z direction and due to loop it will be at -z direction. Hence, option B is correct. For option C: If i1<0 and i2>0 then the magnetic field due to straght line will be in -z direction and due to loop it will also be in -z direction as well, which cancles each other, hence B can not be zero at origin. So, option C is wrong. For option D: z-component is only because of ring which is →B=μ0I2R(−^K) and hence, option D is correct.

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