Electric Field Lines — Question 5

Question 5

Unequal endpoint counts require lines to continue beyond the drawing

A complete field-line convention assigns eight lines per nanocoulomb. A positive charge emits 24 lines. A negative charge absorbs 16 of them. No other finite charges exist; remaining lines extend to infinity.

1. Infer both charges, the net charge and the number of lines reaching infinity.

2. If the drawing normalization changes to twelve lines per nanocoulomb, find all three line counts and explain which physical quantities remain unchanged.

Question 5 - Solution

Unequal endpoint counts require lines to continue beyond the drawing

(a) Method and calculation

$$Q_+=24/8=+3\,\mathrm{nC},\quad Q_-=-16/8=-2\,\mathrm{nC}.$$$$Q_{\mathrm{net}}=+1\,\mathrm{nC},\quad N_\infty=24-16=8.$$

(b) Interpretation and further calculation

$$N_+\prime=36,\quad N_-\prime=24,\quad N_\infty\prime=12.$$$$N_+\prime/N_-\prime=3/2=|Q_+/Q_-|.$$The physical field and charges do not change when more representative lines are drawn.

Physical check

An isolated drawing boundary is not a physical location where a field line may terminate in empty space.