Figure (a) shows that in cross-section, two wires that are straight, parallel, and very long. The ratio $i_1/i_2$ of the current carried by wire $1$ to that carried by wire 2 is $0.25$. Wire $1$ is fixed in place. Wire $2$ can be moved along the positive side of the $x$-axis so, as to change the magnetic energy density $u_{\mathrm{B}}$ set up by the two currents at the origin. Figure (b) gives undefined as a function of the position $x$ of wire $2$. The curve has an asymptote of $u_{\mathrm{\beta }}=1.96 \mathrm{nJ} {\mathrm{m}}^{-3}$ as $x\to \infty$ and the horizontal axis scale is set by $x_{\text{s}}=30.0 \mathrm{cm}$. What is the value of (a) $i_1$ and $\left(\mathrm{b}\right) i_2$?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

In the figure after switch $S$ is closed at time $t=0$, the emf of the source is automatically adjusted to maintain a constant current $i$ through $S$. (a) Find the current through the inductor as a function of time. (b) At what time is the current through the resistor equal to twice the current through the inductor?

In the figure, a rectangular loop of wire with length, $a=2.2 \mathrm{cm}$, width $b=0.80 \mathrm{cm}$ and resistance $R=0.40 \text{mΩ}$ is placed near an infinitely long wire carrying current $i=6.9 \mathrm{A}$. The loop is then moved away from the wire at constant speed $v=3.2 \mathrm{mm} {\mathrm{s}}^{-1}$. When the centre of the loop is at distance $r=1.5 b$ what are (a) the magnitude of the magnetic flux through the loop and (b) the current induced in the loop?

In the figure, a stiff wire bent into a semicircle of radius $a=1.4 \mathrm{cm}$ is rotated at constant angular speed of $30 \mathrm{rev} {\mathrm{s}}^{-1}$ in a uniform $20 \mathrm{mT}$ magnetic field. What are the (a) frequency and (b) amplitude of the emf induced in the loop?