$A$ long straight wire in the horizontal plane carries a current of $50 \; A$ in the north to south direction. Give the magnitude and direction of $B$ at a point $2.5 \; m$ east of the wire.

Two infinitely long thin wires are placed at $(1 \text{ cm}, 0 \text{ cm})$ and $(2 \text{ cm}, 0 \text{ cm})$ as shown in the figure. The same current $i$ flows in both the wires in the same direction, into the page. Let the magnetic field at the origin due to these wires be $\vec{B}$. If $B_0$ is the magnitude of the magnetic field if only the wire at $(1 \text{ cm}, 0 \text{ cm})$ was present, then the value of $B / B_0$ is

Two very long,straight and insulated wires are kept at a $90^o$ angle from each other in the $xy$-plane as shown in the figure. These wires carry a current of equal magnitude $I$,whose directions are shown in the figure. The net magnetic field at point $P$ will be:

$A$ straight wire of length $\pi^2 \, m$ carries a current of $2 \, A$. The magnetic field due to it is measured at a point $1 \, cm$ away from it. If the wire is bent into a circle and carries the same current,what is the ratio of the magnetic field at its centre to the magnetic field measured in the first case?

Give similarity between Biot-Savart law and electrostatic law of Coulomb.

$A$ beam of neutrons performs circular motion of radius $r = 1 \, m$ under the influence of an inhomogeneous magnetic field with inhomogeneity extending over $\Delta r = 0.01 \, m$. The speed of the neutrons is $54 \, m/s$. The mass and magnetic moment of the neutrons are $1.67 \times 10^{-27} \, kg$ and $9.67 \times 10^{-27} \, J/T$ respectively. The average variation of the magnetic field over $\Delta r$ is approximately ....... $T$.