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WBJEETwo infinitely long straight wires lie in the xy - plane along the...
Two infinitely long straight wires lie in the xy - plane along the lines x=±Rx=±R. The wire located at x = +Rx = +R carries a constant current I1I1 and the wire located at x =-Rx =−R carries a constant current I2I2. A circular loop of radius R is suspended with its centre at (0, 0√3R)(0, 0√3R) and in a plane parallel to the xy - plane. This loop carries a constant current II 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 +ˆj+ˆj direction. Which of the following statements regarding the magnetic field →B→B is (are) true?
Solution:
(A)(A) At origin, →B=0→B=0 due to two wires if I1=I2, hence (→Bnet)I1=I2, hence (→Bnet) at origin is equal to →B→B due to ring, which is non-zero.
(B)(B) If I1>0 and I2<0,→BI1>0 and I2<0,→B at origin due to wires will be along +ˆk+ˆk direction and →B→B due to ring is along -ˆk−ˆk direction and hence →B→B can be zero at origin
(C)(C) If I1<0 and I2>0,→BI1<0 and I2>0,→B at origin due to wires is along -ˆk−ˆk and also along -ˆk−ˆk due to ring, hence →B→B cannot be zero (D)(D)
(A)(A) At origin, →B=0→B=0 due to two wires if I1=I2, hence (→Bnet)I1=I2, hence (→Bnet) at origin is equal to →B→B due to ring, which is non-zero.
(B)(B) If I1>0 and I2<0,→BI1>0 and I2<0,→B at origin due to wires will be along +ˆk+ˆk direction and →B→B due to ring is along -ˆk−ˆk direction and hence →B→B can be zero at origin
(C)(C) If I1<0 and I2>0,→BI1<0 and I2>0,→B at origin due to wires is along -ˆk−ˆk and also along -ˆk−ˆk due to ring, hence →B→B cannot be zero (D)(D)
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