Problem — Force between two charged balls

Problem

Two charged balls, one of $+2\ \mu\text{C}$ and one of $-3\ \mu\text{C}$, are $20\ \text{cm}$ apart. Calculate the magnitude and type (attractive or repulsive) of the Coulomb force.

Solution

Data. $q_1 = 2\cdot 10^{-6}\ \text{C}$, $q_2 = 3\cdot 10^{-6}\ \text{C}$ (in magnitude), $r = 0{,}20\ \text{m}$.

Coulomb’s law. The magnitude of the force is:

$F = k\,\frac{|q_1 q_2|}{r^2} = 8{,}99\cdot 10^9 \cdot \frac{(2\cdot 10^{-6})(3\cdot 10^{-6})}{(0{,}20)^2} = 8{,}99\cdot 10^9 \cdot \frac{6\cdot 10^{-12}}{0{,}04} = \frac{0{,}05394}{0{,}04} = 1{,}35\ \text{N}$

Type. The two charges have opposite signs, so the force is attractive: each ball is pulled towards the other.

$\ev{F \approx 1{,}35\ \text{N, attractive}}$

Links

Topics: Electrostatics Concepts: Coulomb’s law