What is the force exerted on 40 micro coulombs by 20 micro coulombs? (charges are separated by 80cm)
F = k•q1•q2/r² =
=9•10^9•40•10^-6•20•10^-6/0.8^2 = ...
To find the force exerted on a charge, we can use Coulomb's Law. Coulomb's Law states that the force between two 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 (9 × 10^9 N*m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, q1 = 40 micro coulombs (40 × 10^(-6) C), q2 = 20 micro coulombs (20 × 10^(-6) C), and r = 80 cm (0.8 m).
Now, let's substitute these values into the Coulomb's Law equation:
F = (9 × 10^9 N*m^2/C^2) * (((40 × 10^(-6) C) * (20 × 10^(-6) C)) / (0.8 m)^2)
Simplifying:
F = (9 × 10^9) * (((40 × 10^(-6)) * (20 × 10^(-6))) / (0.8)^2)
F = (9 × 10^9) * (((40 × 20) × (10^(-6) × 10^(-6))) / (0.64))
F = (9 × 10^9) * ((800 × 10^(-12)) / 0.64)
F = (9 × 10^9) * (8 × 10^(-10) / 0.64)
F = (9 × 10^9) * (8 × 10^(-10)) / (0.64)
F = (9 × 8 × 10^(-9)) / (0.64)
F = (72 × 10^(-9)) / (0.64)
F ≈ 112.5 × 10^(-9)
Therefore, the force exerted on the 40 micro coulomb charge by the 20 micro coulomb charge is approximately 112.5 nano newtons (nN).