$A$ particle carrying a charge equal to $100$ times the charge on an electron is rotating one rotation per second in a circular path of radius $0.8 \ m$. The value of magnetic field produced at the centre will be $(\mu_0 = \text{permeability of vacuum})$

Two concentric and coplanar rings of radius $r$ and $R$ are shown in the figure. Find the magnetic flux linked through the smaller coil when the same current $I$ flows through each in opposite directions $(r << R)$.

The magnetic field at the origin due to a current element $i d l$ placed at a point with vector position $r$ is

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre, the ratio of $i_1: i_2$ is

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 $x = \_\_\_$.
$\left[\text{Use } \mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}\right]$

In the Biot-Savart law,the direction of the magnetic field is determined by which of the following cross products in the expression $d\vec B = \frac{\mu_0}{4\pi} \frac{I d\vec l \times \vec r}{r^3}$?