The magnitude of the electric force between two protons is 2.3 x 10^-26 N. How far apart are they?
Coulombs law applies:
F=kqq/d^2
solve for d
1.58×10^-18
To determine the distance between two protons given the magnitude of the electric force between them, we need to use Coulomb's law. Coulomb's law states that the magnitude of the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
where:
- F is the magnitude of the electric force between the two charges,
- k is the electrostatic constant (approximately 9 x 10^9 N·m^2/C^2),
- q1 and q2 are the charges of the two objects, and
- r is the distance between the centers of the two objects.
Given that the magnitude of the electric force between two protons is 2.3 x 10^-26 N, and considering that the charge of a proton (q1 and q2) is approximately 1.6 x 10^-19 C, we can rearrange the formula to solve for r:
r = sqrt((k * (q1 * q2)) / F)
Substituting the given values, we have:
r = sqrt((9 x 10^9 N·m^2/C^2 * (1.6 x 10^-19 C * 1.6 x 10^-19 C)) / (2.3 x 10^-26 N))
Simplifying this equation will give us the distance between the two protons.