LC Oscillations, Qualitatively — Question 5

Question 5

Charge reversal and energy repetition occur on different time scales

An undamped LC loop begins at maximum positive charge. After one quarter-period all energy is magnetic; after another quarter-period the capacitor is fully charged with reversed polarity. Let T denote a complete state cycle.

1. Compare the charge, current, and energy after T/2 with their initial values.

2. Find the repetition period of each individual field energy.

Question 5 - Solution

Charge reversal and energy repetition occur on different time scales

(a) Method and calculation

$$(q,i)_{t=0}=(Q,0),\quad(q,i)_{T/2}=(-Q,0).$$$$\boxed{U_C(T/2)=U_C(0),\quad q(T/2)\ne q(0)}.$$

(b) Interpretation and further calculation

$$q(t+T/2)=-q(t),\quad i(t+T/2)=-i(t).$$$$\boxed{U_C(t+T/2)=U_C(t),\quad U_L(t+T/2)=U_L(t)}.$$

Physical check

A repeated energy measurement need not indicate a repeated electromagnetic state.