Potential of a 10 nC charge

Calculate the electric potential generated by a point charge $Q = +10$ nC at a distance of $1{,}0$ mm from it. Assume zero potential at infinity.

Solution

Setup. The potential generated by a point charge at distance $r$, with reference zero at infinity, is $V(r) = \frac{kQ}{r}$ Data. $Q = +10 \text{ nC} = 1{,}0\cdot 10^{-8}$ C, $r = 1{,}0 \text{ mm} = 1{,}0\cdot 10^{-3}$ m, $k = 9{,}0\cdot 10^9 \ \text{N m}^2/\text{C}^2$. Substitution. $V = \frac{(9{,}0\cdot 10^9)(1{,}0\cdot 10^{-8})}{1{,}0\cdot 10^{-3}} = \frac{9{,}0\cdot 10^{1}}{1{,}0\cdot 10^{-3}}$ Result. The potential is positive because the charge is positive: $\ev{V = 9{,}0\cdot 10^4 \ \text{V} = 90 \ \text{kV}}$

Links

Topics: Electric field and potential Concepts: Electric potential · Electric charge Skills: Superposition principle Methods: Gradient method Objects: Charged sphere