Q174 / 180 · KCET 2020 · Physics

Two long straight parallel wires are a distance $d$ part. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field $B$ along the line $x x^{\prime}$ is given by

  • A

    Figure
  • Correct answer
    B

    Figure
  • C

    Figure
  • D

    Figure

Solution

The magnetic field in between because of each will be in opposite direction. $B_{\text {in between }}=\frac{\mu_{0} i}{2 \pi x} \hat{\mathbf{j}}-\frac{\mu_{0} i}{2 \pi(2 d-x)}-\hat{\mathbf{j}}$ $=\frac{\mu_{0} i}{2 \pi}\left[\frac{1}{x}-\frac{1}{2 d-x}\right] \hat{\mathbf{j}}$ At $x=d, B_{\text {in between }}=0$ For $x < d, B_{\text {in between }}=\hat{\mathbf{j}}$ For $x>d, B_{\text {in between }}=-\hat{\mathbf{j}}$ Towards $x$, net magnetic field will add up and direction will be $(-\hat{\mathbf{j}})$. Towards $x^{\prime}$, net magnetic field will add up and direction will be $(\hat{\mathbf{j}})$.

Hence, the correct answer is option: 'B'.

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