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(D) The magnetic field due to a long straight wire carrying current $I$ at a distance $r$ is $B = \frac{\mu_0 I}{2 \pi r}$.$(A)$ On the $x$-axis,the d

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All of the above.

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(D) The magnetic field due to a long straight wire carrying current $I$ at a distance $r$ is $B = \frac{\mu_0 I}{2 \pi r}$.$(A)$ On the $x$-axis,the distance from both wires is $r = a$. The magnetic fields are equal in magnitude and opposite in direction,so $B_{net} = 0$. This is correct.$(B)$ On the $y$-axis at $(0, y, 0)$,the distance to the wire at $y=a$ is $|a-y|$ and to the wire at $y=-a$ is $|a+y|$. Using the right-hand rule,the fields are in the $z$-direction. Thus,$B$ has only a $z$-component. This is correct.$(C)$ On the $z$-axis at $(0, 0, z)$,the distance to both wires is $r = \sqrt{a^2 + z^2}$. By symmetry,the $z$-components of the magnetic fields cancel out,and the $y$-components add up. Thus,$B$ has only a $y$-component. This is correct.Since all statements are correct,the answer is $(D)$.

Two long thin,parallel conductors carrying equal currents $I$ in the same direction are fixed parallel to the $x$-axis,one passing through $y = a$ and the other through $y = -a$. The resultant magnetic field due to the two conductors at any point is $B$. Which of the following are correct?

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