Electric Charge — Question 4

Question 4

A neutral pair can be attracted by a nearby charged probe

A neutral model object consists of a fixed $-q$ charge on its near end and $+q$ on its far end. A positive probe lies to its left. The measured attraction on the near end is 6.0 mN; the repulsion on the far end is 2.0 mN. These supplied forces already include the unequal separations.

1. Find the object net charge and net force, taking right as positive. Explain why attraction does not prove negative net charge.

2. Reverse both internal charges without moving anything, keeping the probe positive. Find the new force if each interaction reverses direction with unchanged magnitude.

Question 4 - Solution

A neutral pair can be attracted by a nearby charged probe

(a) Method and calculation

$$Q_{\mathrm{object}}=-q+q=0,\quad F_x=-6.0+2.0=-4.0\,\mathrm{mN}.$$$$|F_{\mathrm{attraction}}|>|F_{\mathrm{repulsion}}|\Rightarrow\text{net force toward probe}.$$

(b) Interpretation and further calculation

$$F_x\prime=+6.0-2.0=+4.0\,\mathrm{mN}.$$$$Q\prime_{\mathrm{object}}=q-q=0.$$The same zero net charge is compatible with different spatial charge arrangements and opposite net forces.

Physical check

The fixed two-charge model illustrates nonuniform interaction; a real induced polarization would respond to the probe rather than remain arbitrarily reversed.