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

The charge of each charge is
`3.02*10^(-19) C`

Step-by-step 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(\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*10^(9)\,(Nm^(2))/(C^(2))`)

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

`F_(e)=k(\mid q^2 \mid)/(r^(2))`

Using the values the problem give us:

`6.7*10^(-9)=8.98755*10^(9)(\mid q^2 \mid)/((3.5*10^(-10))^(2))`

solving for q:

`q=\sqrt{((3.5*10^(-10))^(2)6.7*10^(-9))/(8.98755*10^(9))}`

`q= 3.02*10^(-19) C`