Problem — Potential of a negative charge

Problem

Calculate the electric potential at $50\ \text{cm}$ from a point charge $q = -3\ \mu\text{C}$. Interpret the sign of the result.

Solution

Data. $q = -3\cdot 10^{-6}\ \text{C}$, $r = 0{,}50\ \text{m}$, zero reference at infinity.

Potential of a point charge.

$V = k\,\frac{q}{r} = 8{,}99\cdot 10^9 \cdot \frac{-3\cdot 10^{-6}}{0{,}50} = \frac{-26970}{0{,}5} = -5{,}39\cdot 10^4\ \text{V}$

Interpreting the sign. The potential is negative because the source charge is negative: with the zero reference at infinity, the potential drops below zero as you approach the charge. A positive test charge placed at that point has potential energy $U = q' V < 0$: it is bound (attracted) by the negative charge, and work must be done to take it to infinity.

$\ev{V \approx -5{,}4\cdot 10^4\ \text{V}}$

Links

Topics: Electric field and potential Concepts: Electric potential