Electric Charge — Question 3

Question 3

A network of attractions and repulsions constrains charge signs

Three small objects A, B and C are known to carry nonzero charges and behave as point charges. A is positive. A repels B, and B attracts C. Only electrostatic pair interactions are considered.

1. Infer the signs of B and C, then predict the interaction of A with C. Express the evidence as signs of products of charges.

2. A fourth object D repels C and attracts A. Determine its sign and check that both observations agree. Explain which conclusions would fail if a tested object could be neutral and polarizable.

Question 3 - Solution

A network of attractions and repulsions constrains charge signs

(a) Method and calculation

$$q_A>0,\quad q_Aq_B>0\Rightarrow q_B>0.$$$$q_Bq_C<0\Rightarrow q_C<0,\quad q_Aq_C<0:\ \text{attraction}.$$

(b) Interpretation and further calculation

$$q_Cq_D>0\Rightarrow q_D<0,\quad q_Aq_D<0.$$$$\operatorname{sgn}q_B=+1,\quad\operatorname{sgn}q_C=\operatorname{sgn}q_D=-1.$$Attraction alone does not establish opposite net signs for extended polarizable objects; the stated nonzero point-charge model is essential.

Physical check

Repulsion and attraction are pairwise observations; the signs inferred from all links must be mutually consistent.