Find the resultant magnetic field at the origin due to four infinitely long wires. Each wire produces a magnetic field of magnitude $B$ at the origin.

Write the formula for the magnetic field at a point on the axis of a circular current-carrying loop of radius $R$ at a distance $x$ from its center,where $x >> R$.

An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)

Two identical wires, carrying equal currents are bent into circular coils $A$ and $B$ with $2$ and $3$ turns respectively. The ratio of the magnetic fields at the centres of the coils $A$ and $B$ is

$A$ linear small part of wire $PQ$ is situated on the $y$-axis from $y = -a/2$ to $y = +a/2$, and a current $I$ is flowing through it. The magnetic field produced due to wire $PQ$ at the point $y = +a$ will be:

$A$ horizontal overhead power line is at a height of $4\,m$ from the ground and carries a current of $100\,A$ from east to west. The magnetic field directly below it on the ground is $(\mu _0 = 4\pi \times 10^{-7}\,TmA^{-1})$