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: $\mu_0 = 4\pi \times 10^{-7} \text{ SI units}$)

$A$ long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $a/2$ and $2a$ is:

Two parallel wires in the plane of the paper are at a distance $X_0$ apart. $A$ point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1}=3$, the value of $\frac{R_1}{R_2}$ is:

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have a common axis. The currents through $P$ and $Q$ are $I$ and $4I$ respectively in the clockwise direction as seen from $O$. The net magnetic field at $O$ is:

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?

If a wire of length $L$ carrying a current $i$ is bent in the shape of a semi-circular arc as shown in the figure,then the magnetic field at the centre of the arc is