Two charges are located on the positive x-axis of a coordinate system. Charge q1 = 2.00 × 10^−9C, and it is 0.020 m from the origin. Charge q 2 = –3.00 × 10^ −9 C, and it is 0.040 m from the origin. What is the electric force exerted by these two charges on a third charge, q 3 = 5.00 × 10^−9, located at the origin?
To find the electric force exerted by these two charges on a third charge, we can use Coulomb's Law. Coulomb's Law states that the electric force between two charged particles 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 is the electric 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 scenario, q1 = 2.00 × 10^−9 C, |q2| = 3.00 × 10^−9 C, and q3 = 5.00 × 10^−9C. The distance between q3 and q1 is 0.020 m, while the distance between q3 and q2 is 0.040 m.
Let's calculate the electric force:
For q1:
F1 = (k * |q1| * |q3|) / (r1^2)
= (8.99 × 10^9 N m^2 / C^2) * (2.00 × 10^−9 C) * (5.00 × 10^−9 C) / (0.020 m)^2
For q2:
F2 = (k * |q2| * |q3|) / (r2^2)
= (8.99 × 10^9 N m^2 / C^2) * (3.00 × 10^−9 C) * (5.00 × 10^−9 C) / (0.040 m)^2
To find the net force, or the total force exerted by q1 and q2:
F_net = F1 + F2
Now, we can calculate the values of F1, F2, and F_net.