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 (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 (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{ (Fr^2)/(k) } = \sqrt{ ((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`