Two electrostatic point charges of 83 µC and 50 µC exert a repulsive force on each other of 175 N. What is the distance between the two charges?
3.9
To find the distance between the two charges, we can use Coulomb's Law. Coulomb's Law states that 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 = Force between the charges
k = Coulomb's constant (approximately 9 x 10^9 N·m²/C²)
q1 and q2 = Charges of the two point charges
r = Distance between the charges
In this case, we are given:
q1 = 83 µC = 83 x 10^-6 C
q2 = 50 µC = 50 x 10^-6 C
F = 175 N
k = 9 x 10^9 N·m²/C²
We can rearrange the formula to solve for the distance (r):
r = sqrt((k * (q1 * q2)) / F)
Plugging in the given values:
r = sqrt((9 x 10^9 N·m²/C² * (83 x 10^-6 C * 50 x 10^-6 C)) / 175 N)
Calculating the result:
r = sqrt((9 x 10^9 N·m²/C² * 4.15 x 10^-9 C²) / 175 N)
r = sqrt(3.342 x 10^1 m²)
r = 5.782 m (approximately)
Therefore, the distance between the two charges is approximately 5.782 meters.