Question

"Two identical positive charges exert a repulsive force of 6.7 × 10−9 N when separated by a distance 3.5 × 10−10 m. Calculate the charge of each. The Coulomb constant is 8.98755 × 109 N · m2 /C 2 . Answer in units of C."

Answer 1

Answer:

The charge of each charge is $3.02\times10^{-19} C$

Explanation:

When yo have two charged particles they interact exerting an electrostatic force in the other particles, the magnitude of the electrostatic force between two particles is:

$F_{e}=k\frac{\mid q_{1}q_{2}\mid}{r^{2}}$ (1)

with q1 and q2 the charges, r the distance between them and k the Coulomb's constant ($k=9.0\times10^{9}\,\frac{Nm^{2}}{C^{2}}$)

Because the charges we're dealing are identical positive q1=q2, then (1) is:

$F_{e}=k\frac{\mid q^2 \mid}{r^{2}}$

Using the values the problem give us:

$ 6.7\times10^{-9}=8.98755\times10^{9}\frac{\mid q^2 \mid}{(3.5\times10^{-10})^{2}}  $

solving for q:

$q=\sqrt{\frac{(3.5\times10^{-10})^{2}6.7\times10^{-9}}{8.98755\times10^{9}}}  $

$q= 3.02\times10^{-19} C$