Conductors and Insulators — Question 6

Question 6

Neutralizing an enclosed charge by contact transfers it to the conductor

A neutral isolated hollow conductor encloses a small insulated object with charge $+6.0$ nC. The object initially does not touch the conductor. Use the rule $Q_{\mathrm{inner}}=-q_{\mathrm{cavity}}$ at equilibrium. The object is then allowed to touch and electrically join the conductor; no insulated charged object remains in the cavity.

1. Find initial inner and outer surface charges.

2. Find final conductor net charge and both surface totals after contact. Account for the charge that disappears from the cavity wall.

Question 6 - Solution

Neutralizing an enclosed charge by contact transfers it to the conductor

(a) Method and calculation

$$Q_{{\mathrm{inner}},i}=-6.0\,\mathrm{nC},\quad Q_{{\mathrm{outer}},i}=+6.0\,\mathrm{nC}.$$$$Q_{{\mathrm{conductor}},i}=0,\quad Q_{{\mathrm{entire\ system}},i}=+6.0\,\mathrm{nC}.$$

(b) Interpretation and further calculation

$$Q_{{\mathrm{conductor}},f}=+6.0\,\mathrm{nC},\quad q_{{\mathrm{cavity}},f}=0.$$$$Q_{{\mathrm{inner}},f}=0,\quad Q_{{\mathrm{outer}},f}=+6.0\,\mathrm{nC}.$$On joining the conductor, the object charge and the compensating inner-surface charge cancel in the cavity region. The external surface retains the system net charge.

Physical check

Contact changes the conductor system boundary: its net charge changes even though the larger isolated system charge does not.