A $470$ turn solenoid having a length of $25 \mathrm{cm}$ and a diameter of $10 \mathrm{cm}$ carries a current of $0.29 \mathrm{A}$ . What is the magnitude of the magnetic dipole moment $\overrightarrow{\mu }$ of the solenoid.

 The current-carrying wire loop in figure (a) lies all in one plane and consists of a semicircle of radius $25.0 \mathrm{cm},$a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angle $\mathrm{\theta }$, until it is perpendicular to the plane (figure b). Figure (c) gives the magnitude $B$ of the net magnetic field at the center of curvature versus angle $\mathrm{\theta }$. The vertical scale is set by $B_{\mathrm{a}}=10.0 \mu \mathrm{T}$ and $B_{\mathrm{b}}=12.0 \mu \mathrm{T}.$What is the radius of the smaller semicircle? 

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 $P ?$