An element $dl = dx \hat{i}$ (where,$dx = 1 \, cm$) is placed at the origin and carries a large current $i = 10 \, A$. What is the magnetic field on the $Y$-axis at a distance of $0.5 \, m$?

$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$

Find the magnitude of the magnetic field at point $p$ due to the semi-infinite wire shown below.

Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ and are at a distance $4 \, cm$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires at a distance of $1 \, cm$ from the first wire. The ratio of the two currents and their mutual direction is

Two parallel wires of equal lengths are separated by a distance of $3 \text{ m}$ from each other. The currents flowing through the first and second wire are $3 \text{ A}$ and $4.5 \text{ A}$ respectively in opposite directions. The resultant magnetic field at the midpoint of both the wires is ($\mu_0$ = permeability of free space).

The current of $5 \ A$ flows in a square loop of side $1 \ m$ placed in air. The magnetic field at the centre of the loop is $X \sqrt{2} \times 10^{-7} \ T$. The value of $X$ is . . . . . . .