Two concentric coils each of radius equal to $2\pi \, cm$ are placed at right angles to each other. $3 \, A$ and $4 \, A$ are the currents flowing in each coil respectively. The magnetic induction in $Wb/m^2$ at the centre of the coils will be $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$.

$A$ negative charge is moving towards the observer. What will be the direction of the magnetic field produced by it,as seen by the observer?

Two long wires carrying currents of $8 \,A$ and $6 \,A$ are placed along the $x$-axis and $y$-axis respectively. Find the magnitude of the magnetic field at the point $P(2, 4)$. (Take $\mu_{0} = 4\pi \times 10^{-7} \,T \cdot m/A$)

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$,making an angle $\theta$ with the current element,then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

The magnetic field at the centre of a circular coil of radius $r$,due to current $I$ flowing through it,is $B$. The magnetic field at a point along the axis at a distance $r/2$ from the centre is

Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is