Please help! I want to make sure my answer is correct.
Q:A thundercloud has an electric charge of 43.2 C near the top of the cloud and -38.7 near the bottom of the cloud. The magnitude of the electric force between these two charges is 3.95 x 10^6 N. What is the average separation between these charges? (kc=8.99 x 10^9 N m^2/C^2)
My answer: 1.95 x 10^3 m
To find the average separation between the charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of the 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
In this equation:
F is the force between the charges,
k is the electrostatic constant (kc = 8.99 x 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
We are given:
- |q1| (the magnitude of the charge near the top of the cloud) = 43.2 C
- |q2| (the magnitude of the charge near the bottom of the cloud) = -38.7 C
- F (the magnitude of the electric force between the charges) = 3.95 x 10^6 N
- k (the electrostatic constant) = 8.99 x 10^9 N m^2/C^2
We need to solve for r (the average separation between the charges).
Rearranging the formula, we get:
r = sqrt((k * |q1| * |q2|) / F)
Let's substitute the values into the formula:
r = sqrt((8.99 x 10^9 N m^2/C^2 * 43.2 C * 38.7 C) / (3.95 x 10^6 N))
Using a calculator, we can calculate:
r ≈ 1948.7 m
Therefore, the average separation between the charges is approximately 1948.7 meters.