LC Oscillations, Qualitatively — Question 2

Question 2

The direction of energy flow follows the product of charge and current

At an instant in an ideal LC loop, q is positive and $i=\dot q$ is negative. Use $L\dot i=-q/C$.

1. Determine the signs of both energy rates.

2. If the next observed state has q negative but i still negative, determine which energy store is now growing.

Question 2 - Solution

The direction of energy flow follows the product of charge and current

(a) Method and calculation

$$\dot U_C=(q/C)i<0,\quad\dot U_L=Li\dot i=-qi/C>0.$$$$\boxed{\dot U_C+\dot U_L=0}.$$

(b) Interpretation and further calculation

$$q<0,\ i<0\Rightarrow qi>0.$$$$\boxed{\dot U_C>0,\quad\dot U_L<0}.$$

Physical check

Current direction alone does not identify the direction of energy transfer; capacitor polarity matters too.