Potential Due to a Point Charge — Question 1

Question 1

A negative source is inferred from one voltage measurement

Use $k=8.99\times10^9\,\mathrm{N\,m^2/C^2}$. A lone point charge Q at the origin gives V=-450 V at r=.200 m, with zero potential at infinity.

1. Find Q and the potential at r=.600 m.

2. Find the work by the field moving a $+2.00$ nC probe radially between these points.

Question 1 - Solution

A negative source is inferred from one voltage measurement

(a) Method and calculation

$$Q=Vr/k=\frac{(-450)(.200)}{8.99\times10^9}=-1.00111\times10^{-8}\,\mathrm C.$$$$V(.600)=V(.200)\frac{.200}{.600}=-150\,\mathrm V.$$

(b) Interpretation and further calculation

$$\Delta U=q[-150-(-450)]=+600\,\mathrm{nJ}.$$$$W_e=-\Delta U=-600\,\mathrm{nJ}.$$

Physical check

An outward displacement from a negative source raises the energy of a positive probe.