A thundercloud has an electric charge of 43.2 C near the top of the cloud and -38.7 C near the bottom of the cloud. The magnitude of the electric force between these two charges is 3.95x10^6 N. What is the average separation between these charges? (kc=8.99×10^9 N • m^2/C^2)
Amber, did you get the answer for this?
To find the average separation between the charges, we can use Coulomb's law, which relates the electric force between two charges to their magnitudes and the distance between them.
Coulomb's law is given by:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the magnitude of the electric force between the charges,
- k is Coulomb's constant (kc in this case),
- |q1| and |q2| are the magnitudes of the charges,
- r is the distance between the charges.
We are given:
- F = 3.95x10^6 N,
- |q1| = 43.2 C,
- |q2| = 38.7 C,
- k = 8.99x10^9 N•m^2/C^2.
Let's rearrange the equation to solve for r:
r^2 = (k * (|q1| * |q2|)) / F
First, substitute the given values into the equation:
r^2 = (8.99x10^9 N•m^2/C^2 * (43.2 C * 38.7 C)) / (3.95x10^6 N)
Next, calculate the numerator:
(43.2 C * 38.7 C) = 1670.64 C^2
Now, substitute the calculated value into the equation:
r^2 = (8.99x10^9 N•m^2/C^2 * 1670.64 C^2) / (3.95x10^6 N)
To find r, take the square root of both sides of the equation:
r = √((8.99x10^9 N•m^2/C^2 * 1670.64 C^2) / (3.95x10^6 N))
Simplify the expression:
r ≈ √(3.799393x10^16 m^2) / (3.95x10^6 N)
r ≈ 5.37x10^4 m
Therefore, the average separation between the charges is approximately 5.37x10^4 meters.