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 106 N. What is the average separation between these charges? (kc = 8.99 ×109 N • m2 / C2)

Please help me!?!?!?!?!?!?!? :/

To find the average separation between the charges, we can use the formula for electric force:

F = (k * |q1 * q2|) / r^2

Where:
F is the magnitude of the electric force,
k is the Coulomb's constant (8.99 × 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 scenario, we are given the magnitude of the electric force (F = 3.95 x 10^6 N), the magnitudes of the charges (|q1| = 43.2 C and |q2| = 38.7 C), and we need to find the average separation (r).

First, let's rearrange the formula to solve for r:

r^2 = (k * |q1 * q2|) / F

Now, substitute the given values into the formula:

r^2 = (8.99 × 10^9 N • m^2 / C^2) * (43.2 C * 38.7 C) / (3.95 x 10^6 N)

Calculate the value inside the brackets:

r^2 = (8.99 × 10^9 N • m^2 / C^2) * (1671.84 C^2) / (3.95 x 10^6 N)

Simplify the expression:

r^2 = 3815665696 / 3.95

r^2 = 968830872.4

Take the square root of both sides to find the average separation:

r = √968830872.4

r ≈ 31093.06 m

Therefore, the average separation between the charges is approximately 31093.06 meters.

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

Where:
F is the magnitude of the electric force,
k is the electrostatic constant (k = 8.99 × 10^9 N*m^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.

In this case, we are given the values for the charges (q1 = 43.2 C and q2 = -38.7 C) and the electric force (F = 3.95 x 10^6 N), and we need to find the value of r.

First, rearrange the equation to solve for r:

r = √((k * |q1 * q2|) / F)

Substituting the given values into the equation:

r = √((8.99 × 10^9 N*m^2/C^2 * |43.2 C * -38.7 C|) / (3.95 x 10^6 N))

Now, calculate the value of r using a calculator:

r = √((8.99 × 10^9 N*m^2/C^2 * (43.2 C * 38.7 C)) / (3.95 x 10^6 N))
r ≈ 334.3 meters

The average separation between the charges is approximately 334.3 meters.

Did you find the answer for this?