Potential of a point charge at 1 m

Text

A point charge $Q = +1{,}0\;\mu\text{C}$ is placed in vacuum. Calculate the electric potential at a distance $r = 1{,}0\;\text{m}$ from the charge, assuming $V = 0$ at infinity.

Solution

Formula. The electrostatic potential generated by a point charge at distance $r$, with reference zero at infinity, is $V = k\,\frac{Q}{r}$

Numerical substitution. $V = (9\cdot 10^9\;\text{N}\cdot\text{m}^2/\text{C}^2)\,\frac{1{,}0\cdot 10^{-6}\;\text{C}}{1{,}0\;\text{m}}$

Result. $\ev{V \approx 9{,}0\cdot 10^{3}\;\text{V}}$

The potential is positive, consistent with the positive sign of the charge: approaching $Q$ the potential increases, moving away it tends to zero as $1/r$.

Links

Topics: Electric field and potential Concepts: Electric potential · Electric charge Objects: Charged sphere