$A$ current loop consists of two identical semicircular parts each of radius $R,$ one lying in the $x-y$ plane and the other in the $x-z$ plane. If the current in the loop is $i,$ the resultant magnetic field due to the two semicircular parts at their common centre is

$A$ long straight wire carrying a current of $30 \ A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \ T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \ cm$ away from the wire is $(\mu_0 = 4 \pi \times 10^{-7} \ H/m)$.

$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

In a hydrogen atom,an electron is revolving at $6.6 \times 10^{15} \text{ rev/s}$ around the nucleus in an orbit of radius $0.47 \text{ Å}$. The magnetic field induction produced at the centre of the orbit is nearly: (in $\text{ Wb m}^{-2}$)

Two circular coils $P$ and $Q$ of $100$ turns each have the same radius of $\pi \text{ cm}$. The currents in $P$ and $Q$ are $1 \text{ A}$ and $2 \text{ A}$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular and their centers coinciding. The resultant magnetic field induction at the center of the coils is $\sqrt{x} \text{ mT}$,where $x = \_\_\_$.
$\left[\text{Use } \mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}\right]$

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current $I$ ampere and the radius of the circular loop is $r$ metre. Then the magnetic induction $B$ at the centre $C$ of the circular part is: