Two charges Q1 and Q2 are separated by an unknown distance. They exert a force of 7.6 N on each other. Q1 is 4.4muCand Q2 is 5.5muC. How far apart are the charges in meters?
We can use Coulomb's Law to solve this problem. Coulomb's Law states that the force between two point charges is equal to the product of their charges divided by the square of the distance between them, multiplied by the constant of proportionality, which is equal to 9 x 10^9 Nm^2/C^2.
So, we have the equation:
F = k * (Q1 * Q2)/r^2
Where F is the force, k is the constant of proportionality, Q1 and Q2 are the charges, and r is the distance between the charges.
Plugging in the given values:
7.6 N = (9 x 10^9 Nm^2/C^2) * (4.4 x 10^-6 C) * (5.5 x 10^-6 C) / r^2
Simplifying:
7.6 N = (9 x 10^9 Nm^2/C^2) * (24.2 x 10^-12 C^2) / r^2
Dividing both sides by (9 x 10^9 Nm^2/C^2):
7.6 N / (9 x 10^9 Nm^2/C^2) = (24.2 x 10^-12 C^2) / r^2
Simplifying:
8.44 x 10^-10 m^2/C = (24.2 x 10^-12 C^2) / r^2
To isolate r^2, we can multiply both sides by r^2:
r^2 * 8.44 x 10^-10 m^2/C = 24.2 x 10^-12 C^2
Dividing both sides by (8.44 x 10^-10 m^2/C):
r^2 = (24.2 x 10^-12 C^2) / (8.44 x 10^-10 m^2/C)
Simplifying:
r^2 = 2.87 x 10^-2 m^2
Taking the square root of both sides to solve for r:
r = √(2.87 x 10^-2 m^2)
Calculating:
r ≈ 0.17 m
Therefore, the charges are approximately 0.17 meters apart.