LC Oscillations, Quantitatively — Question 7

Question 7

Current zero crossings reveal a sign ambiguity in a sampled charge

An ideal LC loop has successive current zero crossings separated by .600 ms. At the first crossing q is positive. A charge sensor sampled .200 ms later reads $4.00\,\mu C$.

1. Find the period and maximum charge.

2. Find the charge at the second current zero crossing.

Question 7 - Solution

Current zero crossings reveal a sign ambiguity in a sampled charge

(a) Method and calculation

$$\Delta t_{i=0}=T/2\Rightarrow\boxed{T=1.200\,ms}.$$$$\omega(.200\,ms)=\pi/3,\quad q=Q\cos(\pi/3)=Q/2\Rightarrow\boxed{Q=8.00\,\mu C}.$$

(b) Interpretation and further calculation

$$q(T/2)=Q\cos\pi.$$$$\boxed{q(T/2)=-8.00\,\mu C}.$$

Physical check

Successive current zeros alternate between opposite charge extrema.