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(D) The magnetic field $B$ produced by a long straight wire at a perpendicular distance $r$ is given by $B = \frac{\mu_0}{4\pi} \frac{2I}{r}$.Since th

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Both option $(B)$ and option $(C)$

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(D) The magnetic field $B$ produced by a long straight wire at a perpendicular distance $r$ is given by $B = \frac{\mu_0}{4\pi} \frac{2I}{r}$.Since the current flows along the $x$-axis,the perpendicular distance $r$ of any point $(x, y, z)$ from the wire is $r = \sqrt{y^2 + z^2}$.For point $A(0, 1, 0)$: $r_A = \sqrt{1^2 + 0^2} = 1$.For point $B(0, 1, 1)$: $r_B = \sqrt{1^2 + 1^2} = \sqrt{2}$.For point $C(1, 0, 1)$: $r_C = \sqrt{0^2 + 1^2} = 1$.For point $D(1, 1, 1)$: $r_D = \sqrt{1^2 + 1^2} = \sqrt{2}$.Comparing the distances: $r_A = r_C = 1$ and $r_B = r_D = \sqrt{2}$.Since the magnetic field magnitude depends only on the perpendicular distance $r$,points with the same $r$ will have the same magnetic field magnitude.Thus,$A$ and $C$ have the same magnitude,and $B$ and $D$ have the same magnitude.Therefore,both option $(B)$ and option $(C)$ are correct.

$A$ long straight wire carries a current along the $x$-axis. Consider the points $A(0, 1, 0)$,$B(0, 1, 1)$,$C(1, 0, 1)$,and $D(1, 1, 1)$. Which of the following pairs of points will have magnetic fields of the same magnitude?

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