When point charges q1 = +8.9 µC and q2 = +5.4 µC are brought near each other, each experiences a repulsive force of magnitude 0.71 N. Determine the distance between the charges.
22.5
To determine the distance between the charges, we can use Coulomb's Law, which states that the force between two point 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) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (known as Coulomb's constant) and has the value 8.99 x 10^9 N m^2 / C^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, both charges experience a repulsive force of magnitude 0.71 N. Let's plug in the given values into Coulomb's Law and solve for the distance:
0.71 = (8.99 x 10^9) * (8.9 x 10^-6) * (5.4 x 10^-6) / r^2
Simplifying the equation:
0.71 = (8.99 x 10^9) * (8.9 x 5.4) * (10^-6 x 10^-6) / r^2
0.71 = (8.99 x 8.9 x 5.4) * (10^9 x 10^-12) / r^2
0.71 = (341.18 x 10^-3) / r^2
0.71 = 341.18 x 10^-3 / r^2
Now, let's solve for the distance by rearranging the equation:
r^2 = (341.18 x 10^-3) / 0.71
r^2 = 0.4806
r = √0.4806
r ≈ 0.693 meters
Therefore, the distance between the charges is approximately 0.693 meters.