Question

Determine a que distância devem estar localizadas duas cargas puntiformes idênticas de módulos 2μC, fixas no vácuo, para que a interação entre elas tenha módulo de 30 N.

Answer 1

Força elétrica :

$\displaystyle \text{Fe} = \frac{\text k.\text q_1.\text q_2 }{\text d^2}$

Temos :

$\text{Fe} = 30 \ \text N \\\\ \text q_1=\text q_2 = 2\ \mu\text C =2.10^{-6}\text C$

$\text k = 9.10^9 \ \text N.\text m^2/\text C^2$

Substituindo :

$\displaystyle \text{Fe}=\frac{\text k.\text q_1.\text q_2 }{d^2} \\\\\\ \text 30 = \frac{9.10^9.2.10^{-6}.2.10^{-6}}{\text d^2} \\\\\\ \text d^2 = \frac{36.10^{(9-6-6)}}{30} \\\\\\ \text d^2 = \frac{36.10^{-4}}{3} \\\\\\ \text d = \sqrt{12.10^{-4}} \\\\\\ \huge\boxed{\text d = 2.10^{-2}.\sqrt{3}\ \text m \approx 0,0346 \ \text m } \checkmark$