Charge Is Conserved — Question 6

Question 6

An emission experiment must count returned and escaped electrons

A neutral emitter S sends 1000 electrons to an initially neutral collector C. Later, 200 of those electrons return from C to S and 300 leave C for a distant initially neutral enclosure E. No other particles move. Treat S, C and E as the complete isolated charge system.

1. Find the final charges of S, C and E in units of $e$.

2. Find the final total charge if an observer counts only S and C. Explain the apparent imbalance using the charge crossing that smaller system boundary.

Question 6 - Solution

An emission experiment must count returned and escaped electrons

(a) Method and calculation

$$Q_S=(1000-200)e=+800e.$$$$Q_C=(-1000+200+300)e=-500e,\quad Q_E=-300e.$$$$Q_S+Q_C+Q_E=0.$$

(b) Interpretation and further calculation

$$Q_{S+C}=800e-500e=+300e.$$$$\Delta Q_{S+C}=-Q_{\mathrm{outward}}=-(-300e)=+300e.$$The two-component subsystem becomes positive because electrons leave it. The complete system remains neutral.

Physical check

All three arrows count electrons, so the signed charge carried along each arrow is negative.