At a certain location in the Philippines, Earth's magnetic field of  $39 \mu \mathrm{T}$ is horizontal and directed due north. Suppose the net field is zero exactly $2.0 \mathrm{cm}$ above a long, straight, horizontal wire that carries a constant current. What are the $\left(\mathrm{a}\right)$ magnitude and $\left(\mathrm{b}\right)$ direction of the current?

In figure, point $P_1$ is at a distance, $R=24.0 \mathrm{cm}$ on the perpendicular bisector of a straight wire of length, $L=18.0 \mathrm{cm}$ carrying current $i=58.2 \mathrm{mA}$. (Note that the wire is not long.) What are the (a) magnitude and (b) direction of the magnetic field at $P_1$ due to $i?$ (c) If $R$ is increased, what happens to the magnitude of the field?

Figure (a) shows a length of wire, carrying a current $i$ and bent into a circular coil of one turn. In figure (b), the same length of wire has been bent to give a coil of two turns, each half the original radius.

(a) If $B_{\mathrm{a}}$ and $B_{\mathrm{b}}$ are the magnitudes of the magnetic fields at the centers of the two coils, what is the ratio $\frac{B_{\mathrm{b}}}{B_{\mathrm{a}}}$?

(b) What is the ratio $\frac{{\text{μ}}_{\mathrm{b}}}{{\text{μ}}_{\mathrm{a}}}$ of the dipole moment magnitudes of the coils?

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

In the figure, point $P_2$ is at perpendicular distance, $R=25.1 \mathrm{cm}$ from one end of a straight wire of length, $L=13.6 \mathrm{cm}$ carrying current $i=0.500 \mathrm{A}$. $($Note that the wire is not long.$)$

(a) What is the magnitude of the magnetic field at$P_2$?

(b) If the point of measurement is moved from $P_2$ to $P_1$, does the field magnitude increase, decrease or remain the same?

Consider the equation $B=\frac{{\mu }_{o}i}{2\pi R}$. It gives the magnitude $\mathrm{B}$ of the magnetic field set up by a current in an infinitely long straight wire, at a point $\mathrm{P}$ at perpendicular distance $\mathrm{R}$ from the wire. Suppose that point $\mathrm{P}$ is actually at perpendicular distance $\mathrm{R}$ from the midpoint of a wire with a finite length $\mathrm{L} .$ Using the above equation, calculate $\mathrm{B}$, then results in a certain percentage error. What value must the ratio $\frac{\mathrm{L}}{\mathrm{R}}$ exceed if the percentage error is to be less than $3.00\%?$ That is, what $\frac{L}{R}$ gives

$\frac{(B \text{from the Equation})-(B \text{actual} )}{(B \text{actual })}\left(100\%\right)=3.00\%?$

In figure, four long straight wires are perpendicular to the page and their cross sections form a square of edge length, $a=40 \mathrm{cm}.$ The currents are out of the page in wires $1$ and $4$ and into the page in wires $2$ and$3$ and each wire carries $12 \mathrm{A}$ current. In unit-vector notation, what is the net magnetic field at the square's center?

In figure, part of a long insulated wire carrying current, $i=5.78 \mathrm{mA}$ is bent into a circular section of radius, $R=1.54 \mathrm{cm}$. In unit-vector notation, what is the magnetic field at the center of curvature $C$ if the circular section

(a) lies in the plane of the page as shown and

(b) is perpendicular to the plane of the page after being rotated $90°$ counter-clockwise as indicated?

 In the figure, four long straight wires are perpendicular to the page, and their cross-sections form a square of edge length $a=13.5 \mathrm{cm}$. Each wire carries $7.50 \mathrm{A}$ , and the currents are out of the page in wires $1,3,$ and $4$ and into the page in wire $2 .$ In unit-vector notation, what is the net magnetic force per meter of wire length on wire $4 ?$

In the given figure, four long straight wires are perpendicular to the page and their cross-sections form a square of edge length $a=7.00 \mathrm{cm}.$ Each wire carries $15.0 \mathrm{A}$ and all the currents are out of the page. In unit vector notation, what is the net magnetic force per meter of wire length on wire $1?$