Two electrostatic point charges of +60.0 μC and +57.0 μC exert a repulsive force on each other of 161 N.
What is the distance between the two charges? The value of the Coulomb constant is 8.98755 × 109 N · m2/C2.
Answer in units of m.
To find the distance between the two charges, we can use Coulomb's Law, which states that the 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. We can use the formula:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the charges (given as 161 N)
k is Coulomb's constant (8.98755 × 10^9 N · m^2/C^2)
|q1| and |q2| are the magnitudes of the charges (+60.0 μC and +57.0 μC, respectively)
r is the distance between the charges (what we want to find)
Rearranging the equation to solve for r:
r^2 = k * (|q1| * |q2|) / F
Substituting the given values:
r^2 = (8.98755 × 10^9 N · m^2/C^2) * (60.0 × 10^-6 C) * (57.0 × 10^-6 C) / 161 N
r^2 ≈ 2.5384 × 10^-2 m^2
Taking the square root of both sides:
r ≈ √(2.5384 × 10^-2 m^2)
r ≈ 0.1593 m
Therefore, the distance between the two charges is approximately 0.1593 meters.