Two long thin, parallel conductors carrying equal currents 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?
Diffcult
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$(A)$ $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}-\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}=0$
$(B)$ On $y-axis$ say at $(y, 0,0)$
$B=\frac{-\mu_{0} I}{2 \pi(a+y)} \hat{k}+\frac{\mu_{0} I}{2 \pi(a-y)} \hat{k}$
So except at origin, $B$ has only $z-components$
$B$ cannot has $x-component$ as $B$ is perpendicular to direction of $I .$
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