Answer to Question #108859 in Electricity and Magnetism for Mina

Question

Two elecctrical charges of 500 m(permeability)C each exert a force of 3.2 N on each other. How far apart are they? Next problem. Two electrical charges placed 100 m apart exert a Force of 6200 N on each other. What is the charge? Can anyone give the answer to these physics questions I’m stuck on?

Answer 1

Coulomb's law:

$F_C=k_e \cdot \frac{q_1 \cdot q_2}{r^2}$,

where $F_C$ - Coulomb force, N; $q_1, \; q_2$ - electrical charges, C; $r$ - distance, m; $k_e=9 \cdot 10^9 \; \frac{N \cdot m^2}{C^2}$ - Coulomb's constant. If electrical charges are equal ($q_1=q_2=q$):

$F_C=k_e \cdot \frac{q^2}{r^2}$

1) $r=q \cdot \sqrt{\frac{k_e}{F_C}}$

$r=500 \cdot 10^{-3} \cdot \sqrt{\frac{9 \cdot 10^9}{3.2}} \approx 26516 \; m \approx 26.5 \; km$

2) $q=r \cdot \sqrt{\frac{F_C}{k_e}}$

$q=100 \cdot \sqrt{\frac{6200}{9 \cdot 10^9}} \approx 83 \cdot 10^{-3} \; C = 83 \; mC$