To find the distance between two charges, we can use Coulomb's law, which states that the force between two charges is 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|) / 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, and
r is the distance between the charges.
Given:
|q1| = 2 × 10^-7 C
|q2| = 4.5 × 10^-7 C
F = 0.1 N
k = 8.99 × 10^9 N m^2/C^2
We can rearrange the equation to solve for r:
r^2 = (k * |q1| * |q2|) / F
Plugging in the values:
r^2 = (8.99 × 10^9 N m^2/C^2 * 2 × 10^-7 C * 4.5 × 10^-7 C) / 0.1 N
r^2 = (8.99 × 2 × 4.5) * (10^9 * 10^-7 * 10^-7) / 0.1
r^2 = 80.91 * (10^9 * 10^-7 * 10^-7) / 0.1
r^2 = 80.91 * 10^(-7 + 9 - 1)
r^2 = 80.91 * 10^1
r^2 = 809.1
Taking the square root of both sides:
r = √809.1
r ≈ 28.46
Therefore, the distance between the two charges is approximately 28.46 units.