What must be the distance in meters between point charge q1 = 25.6 µC and point charge q2 = -69.6 µC for the electrostatic force between them to have a magnitude of 8.50 N?
k =9•10^9 N•m²/C²
F=k•q1•q2/r²
r=sqrt(k•q1•q2/F)=
=sqrt(9•10^9•25.6•10^-6•69.6•120^-6/8.5)= .....
To find the distance between point charges q1 and q2 for the electrostatic force between them to have a magnitude of 8.50 N, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The mathematical formula for Coulomb's Law is:
F = k * |q1| * |q2| / r^2
where F is the magnitude of the electrostatic force, k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, we know that the magnitude of the electrostatic force (F) is 8.50 N, q1 = 25.6 µC = 25.6 x 10^-6 C, q2 = -69.6 µC = -69.6 x 10^-6 C, and we need to find the distance between the charges (r).
We rearrange the formula to solve for r:
r = √((k * |q1| * |q2|) / F)
Substituting the given values:
r = √((9 x 10^9 N m^2/C^2 * |25.6 x 10^-6 C| * | -69.6 x 10^-6 C|) / 8.50 N)
r = √((9 x 10^9 N m^2/C^2 * 25.6 x 10^-6 C * 69.6 x 10^-6 C) / 8.50 N)
r = √((9 x 10^9 N m^2/C^2 * 25.6 x 10^-6 C * 69.6 x 10^-6 C) / 8.50 N)
r = √((9 x 25.6 x 69.6 x 10^-11) / 8.50)
r = √(5146.56 x 10^-11 / 8.50)
r = √(605.49 x 10^-11)
r = √(6.0549 x 10^-8)
r = 2.46 x 10^-4 meters
Therefore, the distance between the point charges q1 = 25.6 µC and q2 = -69.6 µC for the electrostatic force between them to have a magnitude of 8.50 N is approximately 2.46 x 10^-4 meters.