Problem — Force between two spheres with equal charge

Problem

Two small spheres carry the same charge $q = 1{,}0\ \mu\text{C}$ and are at a distance $r = 1{,}0\ \text{m}$ in vacuum. Calculate the magnitude of the Coulomb force and state whether it is attractive or repulsive.

Solution

The small spheres are treated as point charges. With $k = 8{,}99\cdot 10^9\ \text{N·m}^2/\text{C}^2$ and $q = 1{,}0\ \mu\text{C} = 10^{-6}\ \text{C}$:

$F = k\,\frac{q^2}{r^2} = 8{,}99\cdot 10^9\cdot\frac{(10^{-6})^2}{(1{,}0)^2} = 8{,}99\cdot 10^9\cdot 10^{-12} = 8{,}99\cdot 10^{-3}\ \text{N} \approx 9{,}0\cdot 10^{-3}\ \text{N}$

The charges have the same sign, so the force is repulsive.

$\ev{F \approx 9{,}0\cdot 10^{-3}\ \text{N (repulsive)}}$

Links

Topics: Elettrostatica Concepts: Legge di Coulomb Objects: Sfera carica