Conductors and Insulators — Question 3

Question 3

Induction can separate opposite charges without grounding

Two initially neutral conducting spheres A and B touch. A positive rod is brought near A, driving electrons from B to A. At this geometry the measured transferred electron charge is $-2.4$ nC. The spheres are separated while the rod remains, then the rod is removed. No object touches the rod or Earth.

1. Find both sphere charges after separation and after removal of the rod.

2. Predict the result if the rod is removed while A and B are still touching and the pair is allowed to equilibrate in a symmetric environment before separation.

Question 3 - Solution

Induction can separate opposite charges without grounding

(a) Method and calculation

$$Q_A=-2.4\,\mathrm{nC},\quad Q_B=+2.4\,\mathrm{nC},\quad Q_A+Q_B=0.$$$$\text{after separation and rod removal}:\quad(Q_A,Q_B)=(-2.4,+2.4)\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$\text{rod removed while connected}:\quad Q_A+Q_B=0,\quad Q_A=Q_B.$$$$Q_A=Q_B=0.$$While connected, electrons can flow back and cancel the separation of charge. Once disconnected, each sphere retains its own net charge.

Physical check

Polarization within a connected neutral pair is different from charging the pair as a whole.