Figure (a) shows, in cross-section, three current-carrying wires that are long, straight, and parallel to one another. Wires $1$ and $2$ are fixed in place on an $x$ axis, with separation $d$ . Wire 1 has a current of $0.750 \mathrm{A}$, but the direction of the current is not given. Wire $3,$ with a current of $0.250 \mathrm{A}$ out of the page, can be moved along the $x$ axis to the right of wire $2 .$ As wire$3$ is moved, the magnitude of the net magnetic force ${\overrightarrow{\mathrm{F}}}_2$ on wire $2$ due to the currents in wires $1$ and $3$ changes. The $x$ component of that force is $F_{2\mathrm{x}}$ and the value per unit length of wire $2$ $\frac{F_{2\mathrm{x}}}{L_2}$ is Figure (b)gives $\frac{F_{2\mathrm{x}}}{L_2}$ versus the position $x$ of wire  $3 .$ The plot has an asymptote$\frac{{\mathrm{F}}_{2\mathrm{x}}}{{\mathrm{L}}_2}=-0.627 \mu \mathrm{N} {\mathrm{m}}^{-1}$ as $x\to \infty .$ The horizontal scale is set by $x_{\mathrm{s}}=24.0 \mathrm{cm}.$ What are the
$\left(\mathrm{a}\right)$ size and
$\left(\mathrm{b}\right)$ direction (into or out of the page) of the current in wire $2 ?$

              

(a)                                                                                    (b)

The given figure shows a cross-section across a diameter of a long cylindrical conductor of radius $\mathrm{r}=2.00 \mathrm{cm}$ Carrying uniform current $170 \mathrm{A}.$ What is the magnitude of the current's magnetic field at radial distance,
$\left(\mathrm{a}\right) 0$
$\left(\mathrm{b}\right)$ $6.00 \mathrm{mm}$
$\left(\mathrm{c}\right)$ $2.00 \mathrm{cm}$ (wire's surface), and
$\left(\mathrm{d}\right)$ $5.90 \mathrm{cm}$ ?

 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 $\mathrm{C}$?