Problem — Electric field of a 5 nanocoulomb charge

Problem

Calculate the electric field generated by a point charge of $+5{,}0\ \text{nC}$ at a distance of $1{,}0\ \text{cm}$.

Solution

The magnitude of the field of a point charge is $E = k\,|q|/r^2$, with $k = 8{,}99\cdot 10^9\ \text{N·m}^2/\text{C}^2$, $q = 5{,}0\cdot 10^{-9}\ \text{C}$ and $r = 1{,}0\cdot 10^{-2}\ \text{m}$:

$E = k\,\frac{|q|}{r^2} = 8{,}99\cdot 10^9 \cdot \frac{5{,}0\cdot 10^{-9}}{(1{,}0\cdot 10^{-2})^2} = \frac{44{,}95}{1{,}0\cdot 10^{-4}} \approx 4{,}5\cdot 10^{5}\ \text{N/C}$

The field is radial, directed outward (positive charge).

$\ev{E \approx 4{,}5\cdot 10^{5}\ \text{N/C}}$

Links

Topics: Campo elettrico e potenziale Concepts: Campo elettrico