Obtain the dimensional formula of (i) ${\epsilon }_0$ (permittivity of vacuum) and (ii) ${\mu }_0$ (permeability of vacuum) in terms of mass $M$, length $L$, time $T$ and electric current $I$.

Two identical circular loops, $P$ and $Q$, each of radius $r$ and carrying currents $I$ and $2I$ respectively are lying in parallel planes such that they have a common axis. The direction of current in both the loops is clockwise as seen from $O$ which is equidistant from the both loops. Find the magnitude of the net magnetic field at point $O$. 

Two identical circular loops, $P$ and $Q$, each of radius $r$ and carrying currents are kept in the parallel planes having a common axis passing through $O$. The dimlion of rurrent in $P$ is clockwise and in $Q$ is anti-clockwise as seen from $O$ which is equidistant from the loops $P$ and $Q$. Find the magnitude of the net magnetic field at $O$.

Two small identical circular loops, marked $\left(1\right)$ and $\left(2\right)$, carrying equal currents, are placed with the geometrical axes perpendicular to each other as shown in Figure. Find the magnitude and direction of the net magnetic field produced at the point $O$.

Figure shows a cube made from a uniform wire. Find the magnetic field at the centre of the cube, if a battery is connected between the points $A$ and $G$.