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Physics · Moving Charges and Magnetic Field

JEE Advanced 2018 — Paper 1 — Question 5

Two infinitely long straight wires lie in the xyx y-plane along the lines x=±Rx= \pm R. The wire located at x=+Rx=+R carries a constant current IlI_{l} and the wire located at x=−Rx=-R carries a constant current I2I_{2}. A circular loop of radius RR is suspended with its centre at (0,0,3R)(0,0, \sqrt{3} R) and in a plane parallel to the xyx y-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 +j^+\hat{j} direction. Which of the following statements regarding the magnetic field B⃗\vec{B} is (are) true?

  1. Option A:

    If I1=I2I_{1}=I_{2}, then B⃗\vec{B} cannot be equal to zero at the origin (0,0,0)(0,0,0)

    Correct
  2. Option B:

    If I1>0I_{1}>0, and I2<0I_{2}<0, then B⃗\vec{B} can be equal to zero at the origin (0,0,0)(0,0,0)

    Correct
  3. Option C:

    If I1<0I_{1}<0, and I2>0I_{2}>0, then B⃗\vec{B} can be equal to zero at the origin (0,0,0)(0,0,0)

  4. Option D:

    If I1=I2I_{1}=I_{2}, then the zz-component of the magnetic field at the centre of the loop is (−μ0I2R)\left(-\frac{\mu_{0} I}{2 R}\right)

    Correct

Answer: A, B, D

Step-by-step solution

(A) If I1=I2\mathrm{I}_{1}=\mathrm{I}_{2}, magnetic field due to infinite wires is equal to zero. So there must be a non-zero magnetic field

at OO due to the current carrying loop.

(B) If I1>0&I2<0I_{1}>0 \& I_{2}<0, magnetic field due to straight lines are along positive z -axis and due to loop it is along

negativez -axis.

(C) If I1<0&I2>0I_{1}<0 \& I_{2}>0 magnetic field due to straight wires are along negative z -axis and due to the loop it is

also along negative z -axis.

(D) B⃗C (along zaxis) =μ0I2R(−k^)\underset{\text { (along zaxis) }}{\vec{B}_{C}}=\frac{\mu_{0} I}{2 R}(-\hat{k})

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2018
Paper
Paper 1
Subject
Physics
Chapter
Moving Charges and Magnetic Field
Topic
Magnetic Field Due to Current-Carrying Wire - Biot-Savart Law

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