In terms of basic units of mass $(M)$,length $(L)$,time $(T)$ and charge $(Q)$,the dimensions of magnetic permeability of vacuum $(\mu_0)$ would be

Two parallel wires in the plane of the paper are at a distance $X_0$ apart. $A$ point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1}=3$, the value of $\frac{R_1}{R_2}$ is:

Two long straight wires are set parallel to each other. Each carries a current $i$ in the same direction and the separation between them is $2r$. The intensity of the magnetic field midway between them is

$A$ closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If the current carried by the wire of the coil is $1\,A$,the value of the magnetic field produced at the centre of the coil will be (permeability of free space $\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A$) nearly:

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

The adjoining figure shows a conductor carrying a current $i$. The magnetic field at the origin is