Two circular coils $A$ and $B$ with their centres lying on the same axis have the same number of turns and carry equal currents in the same sense. They are separated by a distance, have different diameters but subtend the same angle at a point $P$ lying on their common axis. The coil $B$ lies exactly midway between coil $A$ and the point $P$. The magnetic field at point $P$ due to coils $A$ and $B$ is $B_1$ and $B_2$ respectively.

Figure shows a long wire bent at the middle to form a right angle.

The below figure shows two closed paths wrapped around two conducting loops carrying currents $i_1=5.0 \mathrm{A}$ and $i_2=3.0 \mathrm{A}.$ What is the value of the integral $\oint \overrightarrow{\mathrm{B}}·\mathrm{d}\overrightarrow{\mathrm{s}}$ for
(a) path $1$ and (b) path $2$?

Each of the eight conductors in the below figure carries $2.0 \mathrm{A}$ of current into or out of the page. Two paths are indicated for the line integral $\oint \overrightarrow{\mathrm{B}}·d\overrightarrow{\mathrm{s}}.$ What is the value of the integral for$\left(a\right)$ path $1$ and$\left(b\right)$ path $2$?

Three distinct current carrying wires intersect a finite rectangular plane $ABCD$. The current in the left wire and the loop is $I_1$. The direction of current in left-most wire and right-most loop is downwards as shown in the figure. The current $I_2$ through the middle wire is adjusted so that the path integral of the total magnetic field along the perimeter of the rectangle is zero, that is, ${\oint }_{\mathrm{ABCDA}}\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{dl}}=0.$ Then the current $I_2$ is

Rank the value of $\oint \overrightarrow{\mathrm{B}}·d\overrightarrow{\mathrm{I}}$ for the closed paths shown in figure from the smallest to the largest.

Eight wires cut the page perpendicularly at the points shown in figure. A wire labelled with the integer $\mathrm{k}\left(\mathrm{k}=1, 2,\dots , 8\right)$ carries the current $ki$, where $i=2 \mathrm{A}$. For those wires with odd $\mathrm{k}$, the current is out of the page; for those with even $k$, it is into the page. The value of $\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{l}$ along the closed path indicated and in the direction shown.