In the figure two long straight wires (shown in cross section) carry the currents $i_1=30.0 \mathrm{mA}$ and $i_2=50.0 \mathrm{mA}$ directly out of the page. They are equal distances from the origin, where they set up a magnetic field $\overrightarrow{B}$ . To what value must current $i_1$ be changed in order to rotate $\overrightarrow{B}$by $25°$ clockwise? 

In the figure, a wire forms a semicircle of radius $R=9.26 \mathrm{cm}$ and two (radial) straight segments each of length $L=13.1 \mathrm{cm}.$ The wire carries current $i=32.3 \mathrm{mA}$.What is the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at the semicircle's center of curvature $C ?$

The figure shows a snapshot of a proton moving at velocity $\overrightarrow{v}=(-380 \mathrm{m} {\mathrm{s}}^{-1 })\hat{\mathit{j}}$ towards a long straight wire with current, $i=470 \mathrm{mA}$ . At the instant shown, the proton's distance from the wire is $d=2.89 \mathrm{cm}$. In unit-vector notation, what is the magnetic force on the proton due to the current? 

A straight conductor carrying current $i=15 \mathrm{A}$ splits into identical semicircular arcs as shown in the figure. What is the magnetic field at the center $C$ of the resulting circular loop? 

In the figure, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop $1$ has radius $1.50 \mathrm{cm}$ and carries $4.00 \mathrm{m}$$\mathrm{A}$ . Loop $2$ has radius $2.50 \mathrm{cm}$ and carries $6.00 \mathrm{mA}$. Loop $2$ is to be rotated about a diameter while the net magnetic field $\overrightarrow{B}$ set up by the two loops at their common center is measured. (a) Through what angle must loop $2$ be rotated so that the magnitude of that net field is $200 \mathrm{nT}?$ (b) What is the least possible magnitude of the net field?

In the given figure, two circular arcs have radii $a=18.9 \mathrm{cm}$ and $b=10.7 \mathrm{cm}$, subtend angle $\theta =74.0°$, carry current $i=0.411 \mathrm{A}$ and share the same center of curvature $P .$ 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 $P ?$

In the figure, current $i=56.2 \mathrm{mA}$ is set up in a loop having two radial lengths and two semicircles of radii $a=5.72 \mathrm{cm}$ and $b=8.57\mathrm{cm}$ with a common center $P .$ What are the (a) magnitude and (b) direction (into or out of the page) of the magnetic field at $P$ and the (c) magnitude and (d) direction of the loop's magnetic dipole moment? 

A wire with current $i=9.50 \mathrm{A}$ is shown in the figure. Two semi-infinite straight sections, both tangent to the same circle with radius is $1.65 \mathrm{cm}$, are connected by a circular arc that has a central angle $\mathrm{\theta }$ and runs along the circumference of the circle. The arc and the two straight sections all lie in the same plane. If the magnetic field is $B=0$ at the circle's centre, what is $\mathrm{\theta }?$