The magnetic field at the centre of a circular coil of radius $r$,due to current $I$ flowing through it,is $B$. The magnetic field at a point along the axis at a distance $r/2$ from the centre is

$A$ straight section $PQ$ of a circuit lies along the $X$-axis from $x = -\frac{a}{2}$ to $x = \frac{a}{2}$ and carries a steady current $i$. The magnetic field due to the section $PQ$ at a point $x = a$ on the $X$-axis will be:

The magnetic field due to a current-carrying square loop of side $a$ at a point located symmetrically at a distance of $a/2$ from its centre (as shown in the figure) is:

$A$ wire carrying current $i$ is shaped as shown. Section $AB$ is a quarter circle of radius $r$. The magnetic field at the center $C$ is directed:

The magnetic field at the origin due to a current element $i \, d\vec{l}$ placed at position $\vec{r}$ is given by the Biot-Savart Law. Which of the following expressions correctly represent this magnetic field?
$(i) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(ii) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{d\vec{l} \times \vec{r}}{r^3} \right)$
$(iii) \, \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$
$(iv) \, - \left( \frac{\mu_0 i}{4\pi} \right) \left( \frac{\vec{r} \times d\vec{l}}{r^3} \right)$

$A$ wire of resistance $R$ is bent in the form of a square of side $a$ as shown in the figure. Find the magnetic induction at the center of the square $O$ due to the current flowing through it.