Two current carrying loops of radius $R$ and $2 R$ carrying current $I$ and $2 I$ respectively are placed concentrically with their planes at right angle. If magnitude of resultant magnetic field at the centre is $\frac{{\mu }_{0}I}{2R}\sqrt{N}$, then value of $N$ is _____.

Magnetic field at $O$ of a loop of uniform resistance per unit length is ______

Three infinitely long current carrying wires are placed in a plane as shown in figure. The magnetic force (in $N$) on unit length of wire- $2$ is
(Given $\frac{{\mu }_0{I}_0^2}{d}=16\pi$ in $\mathrm{SI}$ unit)

Two current carrying circular loops are placed closely as shown in figure. If integral $\int \overrightarrow{B}·\overrightarrow{dr}$ along axis of the loops within range $-\infty$ to $\infty$ is $N$ times ${\mu }_{0}I$, then value of $N$ is _______

Six parallel infinite wires are placed at the vertices of a regular hexagon. Five wires carry current $I_0$ each while the sixth wire carries current $4I_0$ as shown. The resultant magnetic field at the centre of the hexagon is

A current / flows in a long straight wire with crosssection having the form of a thin quarter-ring of radius $R$ (see figure). The magnetic field $\overrightarrow{B}$ at point $O$ if the current flows out of the page is

A semicircular wire of radius $R$ carrying current $/$ is placed in a magnetic field as shown in the figure. On right hand side of  $yy\text{'}$ the magnetic field is $2B_0,$ outward and on the left hand side it is $B_0$ inward as shown. The magnetic force experience by the wire is

The magnetic field at the centre of dotted circle in the arrangement shown is

The magnetic field at point $P$ in the hollow cylindrical wire carrying a current $i$ shown in the figure at a distance $r$ from axis $(a<r<b)$ is given by (Taking current density to be uniform across its cross-section)