The current passing through a conducting loop in the form of an equilateral triangle of side $4\sqrt{3} \text{ cm}$ is $2 \text{ A}$. The magnetic field at its centroid is $\alpha \times 10^{-5} \text{ T}$. The value of $\alpha$ is . . . . . . . (Given: $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$)

The magnetic induction at the centre $O$ of the current-carrying bent wire shown in the adjoining figure is

Five long wires $A, B, C, D$ and $E$,each carrying current $I$ are arranged to form edges of a pentagonal prism as shown in the figure. Each carries current out of the plane of the paper.
$(a)$ What will be the magnetic induction at a point on the axis $O$? The axis is at a distance $R$ from each wire.
$(b)$ What will be the field if the current in one of the wires (say $A$) is switched off?
$(c)$ What if the current in one of the wires (say $A$) is reversed?

$A$ long straight wire carries a current of $18 \,A$. The magnitude of the magnetic field at a point $12 \,cm$ from it is

Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown in the figure. $AB$ and $CD$ are lines at $45^\circ$ with the axes,with the origin of the axes at $O$. The magnetic field will be zero on the line:

The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is $64$ times the magnetic field at a distance $x$ on its axis from the centre of the coil. Then,the value of $x$ is