When point charges q1=+8.4uC and q2=+5.6uC are brought near each other, each experiences a repulsive force of magnitude 0.66N. Determine the distance between the charges.
To determine the distance between the charges, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges 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 electrostatic force
- k is the electrostatic constant, approximately equal to 9.0 x 10^9 Nm^2/C^2
- |q1| and |q2| are the absolute values of the charges of the two point charges
- r is the distance between the charges
From the given problem, we know the following:
- q1 = +8.4 μC (microCoulombs)
- q2 = +5.6 μC (microCoulombs)
- F = 0.66 N (Newtons)
- k = 9.0 x 10^9 Nm^2/C^2
We need to find the value of r, the distance between the charges.
To solve for the distance, rearrange the formula:
r^2 = k * |q1| * |q2| / F
Simplify by substituting the known values:
r^2 = (9.0 x 10^9 Nm^2/C^2) * (8.4 x 10^-6 C) * (5.6 x 10^-6 C) / (0.66 N)
Now, calculate:
r^2 = (9.0 x 10^9 Nm^2/C^2) * (8.4 x 10^-6 C) * (5.6 x 10^-6 C) / (0.66 N)
r^2 = (42.336 x 10^-15 Nm^2/C^2)
To find r, take the square root of both sides:
r = sqrt(42.336 x 10^-15 Nm^2/C^2)
Now, calculate:
r = sqrt(42.336 x 10^-15) Nm^2/C^2
r = 6.509 x 10^-8 m
Therefore, the distance between the charges is approximately 6.509 x 10^-8 meters or 65.09 nanometers.