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(D) According to the Biot-Savart Law, the magnetic field $d\vec{B}$ produced by a current element $I d\vec{l}$ at a position vector $\vec{r}$ is given

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Zero

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(D) According to the Biot-Savart Law, the magnetic field $d\vec{B}$ produced by a current element $I d\vec{l}$ at a position vector $\vec{r}$ is given by $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} 	imes \vec{r})}{r^3}$.Here, the wire $PQ$ lies along the $y$-axis, so the current element $I d\vec{l}$ is directed along the $y$-axis (i.e., $\vec{dl} = dy \hat{j}$).The point of observation is at $y = +a$ on the $y$-axis, so the position vector $\vec{r}$ from any point $y$ on the wire to the observation point is $\vec{r} = (a - y) \hat{j}$.Since the cross product of two parallel vectors is zero, $d\vec{l} 	imes \vec{r} = (dy \hat{j}) 	imes ((a - y) \hat{j}) = 0$.Therefore, the magnetic field at any point lying on the axis of a straight current-carrying wire is zero.

$A$ linear small part of wire $PQ$ is situated on the $y$-axis from $y = -a/2$ to $y = +a/2$, and a current $I$ is flowing through it. The magnetic field produced due to wire $PQ$ at the point $y = +a$ will be:

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