Two positive charges with the same magnitude are one meter apart. Find the magnitude of the charges if the force between them is one Newton.
F=kq1q2/1^2
solve for q if they are equal.
how do you know what to plug into the equation?
To find the magnitude of the charges, we can use Coulomb's Law, which describes the force between two charged particles. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = (k * q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (k = 8.99 * 10^9 N m^2 / C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
Given that the force between the charges is 1 Newton (F = 1 N) and the distance between them is 1 meter (r = 1 m), we can rearrange Coulomb's Law to solve for the charges' magnitudes.
1 = (k * q1 * q2) / 1^2
1 = k * q1 * q2
Since the charges have the same magnitude (q1 = q2 = q), we can rewrite the equation as:
1 = k * q^2
Solving for q, we divide both sides of the equation by k:
q^2 = 1 / k
Taking the square root of both sides, we get:
q = √(1 / k)
Now we can substitute the value of k (k = 8.99 * 10^9 N m^2 / C^2) into the equation:
q = √(1 / 8.99 * 10^9 N m^2 / C^2)
Using a calculator, we can evaluate this expression:
q ≈ 3.162 * 10^(-10) C
Therefore, the magnitude of the charges is approximately 3.162 * 10^(-10) Coulombs.