In figure (a), two circular loops, with different currents but the same radius of $2.0 \mathrm{cm},$ are centered on a $y$ axis. They are initially separated by distance $L=6.0 \mathrm{cm},$ with loop $2$ positioned at the origin of the axis. The currents in the two loops produce a net magnetic field at the origin, with $y$ component $B_{\mathrm{y}}.$ That component is to be measured as loop $2$ is gradually moved in the positive direction of the $y$ axis. Figure (b) gives $B_{\mathrm{y}}$ as a function of the position $y$ of loop $2 .$The curve approaches an asymptote of $B_{\mathrm{y}}=7.20 \mu \mathrm{T}$ as $y\to \infty .$ The horizontal scale is set by $y_{\mathrm{s}}=10.0 \mathrm{cm}$ What are (a) current $i_1$ in loop $1$ and (b) current $i_2$ in loop $2?$

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

A student makes a short electromagnet by winding $280$ turns of wire around a wooden cylinder of diameter $d=5.0 \mathrm{cm}.$ The coil is connected to a battery producing a current of $3.8 \mathrm{A}$ in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance $z \gg d$ will the magnetic field have the magnitude $5.0 \mu \mathrm{T}$ (approximately one-tenth that of Earth's magnetic field)? 

The figure shows, in cross-section, two long straight wires held against a plastic cylinder of radius$15.0 \mathrm{cm}$. Wire $1$ carries current $i_1=60.0 \mathrm{mA}$ out of the page and is fixed in place at the left side of the cylinder. Wire $2$ carries current $i_2=40.0 \mathrm{mA}$ out of the page and can be moved around the cylinder. At what (positive) angle ${\mathrm{\theta }}_2$ should wire $2$ be positioned such that, at the origin, the net magnetic field due to the two currents has magnitude $80.0 \mathrm{nT}$?

In the figure two long straight wires are perpendicular to the page and separated by distance $d_1=0.75 \mathrm{cm}.$ Wire $1$ carries $6.5 \mathrm{A}$ into the page. What are the 

(a) magnitude and 

(b) direction (into or out of the page) of the current in wire $2$ if the net magnetic field due to the two currents is zero at point $P$ located at distance $d_2=2.50 \mathrm{cm}$ from wire $2$? If the current in wire $2$ is then reversed, what will be the 

(c) magnitude and 

(d) direction of the net field at point $P ?$ 

In the figure (a), wire $1$ consists of a circular arc and two radial lengths; it carries current $i_1=0.20 \mathrm{A}$ in the direction indicated. Wire $2,$ shown in cross-section, is long, straight, and perpendicular to the plane of the figure. Its distance from the centre of the arc is equal to the radius $R$ of the arc, and it carries a current $i_2$ that can be varied. The two currents set up a net magnetic field $\overrightarrow{B}$ at the centre of the arc. Figure (b) gives the square of the field's magnitude $B^2$ plotted versus the square of the current $i_2^2$ .The vertical scale is set by $B_{\mathrm{s}}^2=10.0\times {10}^{-10} {\mathrm{T}}^2.$What angle is subtended by the arc? 

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

 In the figure, current $i=2.2 \mathrm{A}$ is set up in a long hairpin conductor formed by bending a wire into a semicircle of radius $R=8.5 \mathrm{mm}$ . Point $b$ is midway between the straight sections and so distant from the semicircle that each straight section can be approximated as being an infinite wire. What are the (a) magnitude and (b) direction (into or out of the page) of $\overrightarrow{B}$ at $a$ and the (c) magnitude and (d) direction of $\overrightarrow{B}$ at $b?$

A current is set up in a wire loop consisting of a semicircle of radius $4.50 \mathrm{cm},$ a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure a shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is $47.25 \mu \mathrm{T}$ . The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane (Fig. b).The magnetic field produced at the (same) center of curvature now has magnitude $15.75 \mu \mathrm{T},$ and its direction is reversed from the initial magnetic field. What is the radius of the smaller semicircle? 

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

The figure shows two current segments. The lower segment carries a current of $i_1=0.40 \mathrm{A}$ and includes a semicircular arc with radius $5.0 \mathrm{cm},$ angle $180°,$ and center point $P$. The upper segment carries current $i_2=3i_1$ and includes a circular arc with radius $4.0 \mathrm{cm},$ angle $120°,$ and the same center point $P .$ What is the (a) magnitude and (b) direction of the net magnetic field $\overrightarrow{B}$ at $P$ for the indicated current directions? What are the (c) magnitude and (d) direction of $\overrightarrow{B}$ if $i_1$ is reversed? 

The figure (a) shows two wires, each carrying a current. Wire $1$ consists of a circular arc of radius $R$ and two radial lengths; it carries current $i_1=1.5 \mathrm{A}$ in the direction indicated. Wire $2$ is long and straight; it carries a current $i_2$ that can be varied; and it is at distance $\frac{R}{2}$ from the centre of the arc. The net magnetic field $\overrightarrow{B}$ due to the two currents is measured at the centre of curvature of the arc. Figure (b) is a plot of the component of $\overrightarrow{B}$ in the direction perpendicular to the figure as a function of current $i_2.$ The horizontal scale is set by $i_{2\mathrm{s}}=1.00 \mathrm{A}$ What is the angle subtended by the arc?