Two electrostatic point charges of +30 ìC and +25 ìC exert a repulsive force of 200 N on each other. What is the distance between the two charges?
To find the distance between two charges, we can use Coulomb's Law, which 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.
The formula for Coulomb's Law is:
F = k * q1 * q2 / r²
Where:
F is the force between the charges,
k is the electrostatic constant (9 x 10^9 N·m²/C²),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, we have:
F = 200 N (repulsive force),
q1 = +30 μC (charge 1),
q2 = +25 μC (charge 2), and
we need to find r (distance between the charges).
Let's plug in the values into the formula and solve for r:
F = k * q1 * q2 / r²
200 N = (9 x 10^9 N·m²/C²) * (30 x 10^-6 C) * (25 x 10^-6 C) / r²
Now, let's rearrange the formula to solve for r:
r² = (k * q1 * q2) / 200 N
r² = ((9 x 10^9 N·m²/C²) * (30 x 10^-6 C) * (25 x 10^-6 C)) / 200 N
Simplifying:
r² = 3.375 x 10⁻³ m²
Taking the square root of both sides to solve for r:
r = √(3.375 x 10⁻³) m
r ≈ 0.058 m
The distance between the two charges is approximately 0.058 meters.