small, center coil. $($Note: even though I$\text{'}$m not asking for the direction of the field in your final answer, you'll still have to think about directions to get to that final answer.$)$

$9)$ When you plug in a device like a computer, often there is a transformer box on the cable to lower the rms voltage to about $12$ volts. Explain how such a transformer would work, at the detailed level of charges$/$currents$/$fields$.($Probably will require $\backslash (\backslash$sim $3\backslash )$ sentences.$)$ Give the relevant parameters to make sure it would end up at $12$ volts if using an ordinary outlet.

$10)$ You want to power a device that normally uses a $9$ Volt battery, but you only have two $1\mathrm{.}5$ Volt batteries. You hook these batteries together and run them into a $1$:$3$ step$-$up transformer. Why doesn't this work to power your device? Explain $*$exactly$*$ where things go wrong for full credit.

Longer Problems

$(1)$ Two long wires carry current into the page $($marked by $\backslash (\backslash$mathrm$\{$X$\}^\{\backslash$prime$\}\backslash$mathrm$\{$s$\}\backslash ))$ on two corners of a $1$ cm by $1$ cm square. At another corner $(1$ cm from each wire$),$ a charged particle with $\backslash ($ Q$=1\backslash$mathrm$\{$nC$\}\backslash )$ is moving into the page at a speed of $\backslash (100\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

A$)$ Find the magnitude and general direction of the force on the moving charge.

B$)$ Find the magnitude and the force on one wire due to the other wire. $($Ignore the moving charge for this part$).$

C$)$ Discuss how$+$why the amount of force you got for part A can be so much smaller than the force for part B $,$ even though the average speed of a moving charge in a currentcarrying wire is much smaller than $\backslash (100\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$(2)$ A $4-$ohm lightbulb is connected to a tiny coil of $2000$ loops of wire. Each loop has a $2$ mm radius. The coil is positioned $1$ cm away from a long straight wire. The long straight wire has $10$ ohms of resistance, and is connected to a standard wall outlet $($eventually forming a complete circuit$).$

A$)$ Show exactly how the long straight wire could be positioned next to the tiny coil $(1$ cm away$)$ such that the bulb will light, even without a direct connection. Explain any directions or