LC Oscillations, Qualitatively — Question 3

Question 3

One charge measurement leaves two possible directions of motion

An ideal LC oscillator has maximum charge Q. At a particular instant its charge is $q=3Q/5$. Let $I_{\max}=Q/\sqrt{LC}$.

1. Find the electric and magnetic energy fractions and possible currents.

2. What additional sign measurement distinguishes charging from discharging at that instant?

Question 3 - Solution

One charge measurement leaves two possible directions of motion

(a) Method and calculation

$$U_C/U=(q/Q)^2=9/25,\quad U_L/U=1-9/25=16/25.$$$$\boxed{i=\pm4I_{\max}/5}.$$

(b) Interpretation and further calculation

$$\dot U_C=qi/C:\quad i>0\Rightarrow\dot U_C>0.$$$$\boxed{i<0:\ \text{discharging};\qquad i>0:\ \text{charging}}.$$

Physical check

The same capacitor charge occurs twice per cycle with opposite currents.