Eight wires cut the page perpendicularly at the points shown in figure. A wire labelled with the integer $\mathrm{k}(\mathrm{k}=1,2,\dots ,8)$ Carries the current $ki$ , where $i=6.00 \mathrm{mA}$. For those wires with odd$k,$ the current is out of the page; for those with even$\mathrm{k},$ it is into the page. Evaluate$\oint \overrightarrow{\mathrm{B}}·\mathrm{d}\overrightarrow{\mathrm{s}}$ Along the closed path indicated and in the direction shown.

 Each of the eight conductors in the given figure carries $5.0 \mathrm{A}$ of current into or out of the page. Two paths are indicated for the line integral$\oint \overrightarrow{B}·\mathrm{d}\overrightarrow{s}.$ What is the value of the integral for $\left(\mathrm{a}\right)$ path$1$ and $\left(\mathrm{b}\right)$ path $2 ?$

In the given figure a long circular pipe with outside radius $R=2.6 \mathrm{cm}$ carries a (uniformly distributed) current $i=2.12 \mathrm{mA}$ into the page. A wire runs parallel to the pipe at a distance of $3.00 R$ from centre to centre. Find the $\left(\mathrm{a}\right)$ magnitude and $\left(\mathrm{b}\right)$ the direction (into or out of the page) of the current in the wire such that the net magnetic field at point$P$ has the same magnitude as the net magnetic field at the center of the pipe but is in the opposite direction.

In the given figure, two semicircular arcs have radii $R_2=7.80 \mathrm{cm}$ and $R_1=2.86 \mathrm{cm},$ that carry current $i=0.281 \mathrm{A}$ and have the same centre of curvature $\mathrm{C} .$ What are the $\left(\mathrm{a}\right)$ magnitude and $\left(\mathrm{b}\right)$ direction (into or out of the page) of the net magnetic field at $\mathrm{C}$? 

The figure shows two very long straight wires (in cross-section) that each carry a current of $4.00 \mathrm{A}$ directly out of the page. Distance $d_1=6.00 \mathrm{m}$ and distance $d_2=8.00 \mathrm{m}.$ What is the magnitude of the net magnetic field at point $\mathrm{P}$, which lies on a perpendicular bisector to the wires?

Figure (a) shows an element of length $ds=1.00 \mathrm{\mu m}$ in a very long straight wire carrying current. The current in that element sets up a differential magnetic field $d\overrightarrow{\mathit{B}}$ at points in the surrounding space. Figure (b) gives the magnitude $dB$ of the field for points $3.5 \mathrm{cm}$ from the element, as a function of angle $\mathrm{\theta }$ between the wire and a straight line to the point. The vertical scale is set by $d{B}_{\mathrm{s}}=120 \mathrm{pT}$. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance $3.5 \mathrm{cm}$ from the wire?

                          $\mathrm{Fig}-\left(\mathrm{a}\right) \mathrm{Fig}-\left(\mathrm{b}\right)$