= Physics 212 Discussion Notes: Week 7 = == RC Circuits and the Lorentz Force == === Discussion Material === * [0:00] Your mini-lecture on RC circuits and Lorentz force * [0:15] Discussion Questions A (RC circuits) , B (Lorentz force) and C (second RC circuit problem) * [1:30] Quiz 5 === Suggestions for Mini-Lecture === This week, we have two distinct subjects to cover: RC circuits, and the Lorentz force. You’ll thus have to give a mini-lecture on both topics. For '''''RC circuits''''', first draw the simplest possible RC circuit (shown in the figure). Then I would suggest discussing these key points: * '''Qualitative description''': First, describe qualitatively ''what happens'' when you throw the switch in your RC circuit. *# Initially, the capacitor is uncharged. *# Throw the switch to position a  current flows and charge ''Q'' builds up on the capacitor plates. *# After a long time, the capacitor is fully charged and can accept no more. *# Throw the switch to position b  current flows again, in the opposite direction, and the capacitor discharges. * '''Asymptotic behavior of a capacitor''': ** When a capacitor is completely ''discharged'', it looks like a ''wire''  charge is free to accumulate on its empty plates, so it offers no impediment to the flow of current ** When a capacitor is ''fully charged'', it looks like an ''open break'' in the circuit  it’s fully charged, so it blocks the flow of current. * '''Charging and discharging solutions''': The time-dependence of the charge ''Q''(''t'') on the capacitor. has two solutions: Sketch the behavior of these two solutions on the board. Mark the approximate location of ''t'' = '''''''' on your graphs to give an idea of its significance  it determines the ''time scale'' of the charging/discharging procedure. Encourage the students to ''redraw'' their circuits whenever they are asked a question about the time-zero or time-infinity state of the circuit. For the '''''Lorentz force''''' part of your mini-lecture: * '''Magnetic fields''': For now we’ll just say that magnetic fields come from the north and south poles of a bar magnet, in much the same way that electric fields come from + and – charges. (The microscopic origin of magnetic fields = currents will come next week.) * '''The Lorentz Force''' : This formula describes the measurable ''effect'' of magnetic fields  they exert forces on ''moving charges''. In particular, ** ''B''-fields only exert a force on charges when they are moving in a direction ''perpendicular'' to the ''B'' field. ** The force is ''perpendicular'' to both the charge’s velocity and the ''B''-field, via the right-hand rule. Illustrate all this with a drawing on the board. First establish a coordinate system, then draw a uniform '''''B''''' field in the +''z'' direction. Show what the force would be on a positive charge moving in the +''x'', +''y'', and +''z'' directions. * '''Circular orbits''': Continue your illustration of the action of the Lorentz force by showing that as a charge continues to move in a ''B'' field , its trajectory ''turns'', and the force on it ''also turns''. The result is circular motion, with radius ''R'' = ''mv''/''qB''. They will derive this key formula in DQB. * Since the Lorentz force is always ''perpendicular'' to a particle’s trajectory, '''magnetic forces do
no work'''. That means that the kinetic energy, and therefore the velocity, of a particle orbiting in a ''B'' field remains ''constant''. === Other notes === We try to eliminate “propagation” from the quizzes = questions whose answers depend on the successful solution of a previous question. However, it is not always possible. We will only have 3 quiz choices this week A,C,D because of excessive propagation of error but I notice some possible propagation of error on quiz A as well. Just watch it as you are grading.