Gind the force between charges of +10.o uC and -50.0 uC located 20.0 cm apart
To find the force between two charges, we can use Coulomb's law. Coulomb's law states that the force between two charges is equal to the product of their magnitudes, divided by the square of the distance between them, multiplied by a constant known as the electrostatic constant.
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 (k = 8.99 * 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, we have two charges: +10.0 uC and -50.0 uC, located 20.0 cm (0.20 m) apart.
First, we need to convert the charges to coulombs. 1 uC (microcoulomb) is equal to 10^-6 C (coulomb).
|q1| = 10.0 uC = 10.0 * 10^-6 C = 1.0 * 10^-5 C
|q2| = 50.0 uC = 50.0 * 10^-6 C = 5.0 * 10^-5 C
Plugging in the values into Coulomb's law, we get:
F = (8.99 * 10^9 N·m^2/C^2) * ((1.0 * 10^-5 C) * (5.0 * 10^-5 C)) / (0.20 m)^2
Simplifying the equation gives:
F = (8.99 * 10^9 N·m^2/C^2) * (5.0 * 10^-10 C^2) / (0.20 m)^2
Calculating the numerator:
(8.99 * 10^9 N·m^2/C^2) * (5.0 * 10^-10 C^2) = 4.495 * 10^-1 N·m^2
Calculating the denominator:
(0.20 m)^2 = 0.04 m^2
Substituting the calculated values back into the equation:
F = 4.495 * 10^-1 N·m^2 / 0.04 m^2
F = 11.24 N
Therefore, the force between the two charges is 11.24 Newtons.
Coulombs Law of repulsion:
F=k q1*q2/distance^2 change units to meters, coulumbs.