Potential Due to a Point Charge — Question 2

Question 2

Potential and field together locate an unseen point source

Use $k=8.99\times10^9\,\mathrm{N\,m^2/C^2}$. At P, a single point charge produces V=180 V and field magnitude E=600 V/m. The potential zero is at infinity.

1. Find the distance from P to the source and the source charge.

2. If the measured field at P points east, locate the source relative to P; explain why a voltage offset would spoil the distance inference.

Question 2 - Solution

Potential and field together locate an unseen point source

(a) Method and calculation

$$V=kQ/r,\quad E=k|Q|/r^2\Rightarrow r=|V|/E=.300\,\mathrm m.$$$$Q=Vr/k=6.00667\,\mathrm{nC}>0.$$

(b) Interpretation and further calculation

$$\mathbf E\text{ points away from }Q>0\Rightarrow Q\text{ lies }.300\,\mathrm m\text{ west of P}.$$$$V_{\mathrm{measured}}=kQ/r+C\Rightarrow |V_{\mathrm{measured}}|/E\ne r\quad\text{in general}.$$

Physical check

The inversion uses both the single-source model and its infinity reference.