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).

Find the magnetic field at the centre $P$ of a square loop of side length $20 \, cm$ carrying a current of $3 \, A$.

Two mutually perpendicular conductors carrying currents $I_1$ and $I_2$ lie in one plane. The locus of the point at which the magnetic induction is zero,is a

The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ from an element carrying current $i$ is given by:

$A$ current-carrying loop $ABCD$ has two circular arcs $AD$ and $BC$ with radii $1 \text{ cm}$ and $2 \text{ cm}$ respectively, as shown in the figure. The two arcs $AD$ and $BC$ subtend a common angle of $30^{\circ}$ at the centre $O$. If the current flowing in the loop is $\frac{1.2}{\pi} \text{ A}$, then the magnitude of the net magnetic field at $O$ is (Given $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$): (in $\mu \text{T}$)

Let the current $I$ be associated with an electron of charge $e$ moving in a circular orbit of radius $r$ with speed $v$ around the positively charged nucleus. The ratio $\frac{r}{v}$ is