Two infinitely long straight wires lie in the xy - plane along the lines x = ± R . The wire located at…

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?
  1. If I1=I2, then B→ cannot be equal to zero at the origin 0, 0, 0
  2. If I1>0 and I2<0, then B→ can be equal to zero at the origin 0, 0, 0
  3. If I1<0 and I2>0, then B→ can be equal to zero at the origin 0, 0, 0
  4. If I1=I2 , Then the z-component of the magnetic field at the centre of the loop is \((-\mu 0 \mathrm{I} / 2 \mathrm{R})\)

Solution

(A) At origin, B→=0 due to two wires if I1=I2, hence B→net 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) \(\underset{\text { (along z axis) }}{\vec{B}_C}=\frac{\mu_0 I}{2 R}(-\hat{k})\)

Asked in: JEE Advanced 2018 (Paper 1)

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