A Gaussian surface encloses two charges. The total electric flux through the Gaussian surface is 8.3 x 106 N m2/C. If one of the charges is -14.9 micro-Coulombs and the magnitude of the electric force between them is 2.76 Newtons, what is the distance between the charges in meters?
Use the total flux and Gauss' law to get the total charge inside the enclosing surface.
From the value of one charge, and the sum from the first step, get the other charge.
From the force and the values of the two charges, get the separation R using Coulomb's law.
To find the distance between the charges, we can use Coulomb's law to relate the electric force between the charges to their magnitudes and the distance between them.
Coulomb's law states that the electric force between two charges is given by the equation:
F = (k * |q1 * q2|) / r^2
where F is the electric force between the charges, k is the electrostatic constant (k = 8.99 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.
Given that the electric force between the charges is 2.76 Newtons and one of the charges is -14.9 micro-Coulombs (-14.9 x 10^-6 C), we can rearrange the equation to solve for the distance:
r = √((k * |q1 * q2|) / F)
Plugging in the values we have:
r = √((8.99 x 10^9 N m^2/C^2 * |(14.9 x 10^-6 C) * (14.9 x 10^-6 C)|) / (2.76 N))
Now we can calculate the distance by evaluating this expression.