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 3.95 x 10 ^6 N. What is the average separation between these charges?
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Sure, I can help you with that!
To find the average separation between two charges, we can use the equation for electric force:
F = (k * |q1 * q2|) / r^2
where F is the magnitude of the electric force, k is the electrostatic constant (9 x 10^9 N m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the separation between the charges.
In this case, the magnitude of the electric force is given as 3.95 x 10^6 N, and the magnitudes of the charges are 43.2 C and 38.7 C.
Now, we need to rearrange the equation to solve for r:
r^2 = (k * |q1 * q2|) / F
Plugging in the given values and solving for r:
r^2 = ((9 x 10^9 N m^2/C^2) * (43.2 C * 38.7 C)) / (3.95 x 10^6 N)
r^2 = (1511.52 N m^2/C^2) / (3.95 x 10^6 N)
r^2 = 0.383 N m^2/C^2
Taking the square root of both sides, we find:
r ≈ sqrt(0.383) ≈ 0.62 m
Therefore, the average separation between these charges is approximately 0.62 meters.