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 charged particle $(q, m)$ is projected with velocity $v_0\hat{i}$ towards a circular region of uniform magnetic field $B$ perpendicular and into the plane of paper as shown in the figure. $C$ is the centre of the circular region. If the angle between the line $CA$ and the $x-$ axis is $37°$ and the particle passes through point $C$ then the radius of the circular region $R$ is

The figure shows the path of a proton that passes through two regions containing uniform magnetic fields of magnitude $B_1$ and $B_2.$ Its path in each region is a half circle. Then

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)