Question

Two identical positive charges exert a repulsive force of 6.2 × 10−9 n when separated by a distance 3.7 × 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

The electrostatic force between two charges is given by
$F=k \frac{q_1 q_2}{r^2}$
where
k is the Coulomb's constant
q1 and q2 are the two charges
r is their separation

In this problem, the two charges are identical, so we can call them q1=q2=q, and the formula becomes
$F=k \frac{q^2}{r^2}$

Since we know the magnitude of the force and the separation between the two charges, we can re-arrange the equation to find the value of each charge:
$q= \sqrt{ \frac{Fr^2}{k} } = \sqrt{ \frac{(6.2 \cdot 10^{-9} N)(3.7 \cdot 10^{-10}m)^2}{8.99 \cdot 10^9 Nm^2C^{-2}} }=3.07 \cdot 10^{-19} C$