In a thundercloud there may be an electric
charge of 18 C near the top of the cloud and
−18 C near the bottom of the cloud.
If these charges are separated by about
7 km, what is the magnitude of the elec-
tric force between these two sets of charges?
The electric force constant is 8.98755 ×
109 N · m2/C2.
Answer in units of N.
F=kqq/s^2
To calculate the magnitude of the electric force between two charges, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two charges is equal to the product of the charges divided by the square of the distance between them, multiplied by the electric force constant.
The formula for the magnitude of the electric force (F) is given by:
F = (k * |q1 * q2|) / (r^2)
where F is the magnitude of the electric force, k is the electric force constant (k = 8.98755 × 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 case, the magnitude of the charges are 18 C and -18 C, and the distance between them is 7 km or 7000 m.
Let's substitute these values into the formula:
F = (8.98755 × 10^9 N • m^2/C^2 * |18 C * -18 C|) / (7000 m)^2
First, we take the absolute value of the charges to ensure we have positive values:
F = (8.98755 × 10^9 N • m^2/C^2 * 18 C * 18 C) / (7000 m)^2
Now, we simplify:
F = (8.98755 × 10^9 N • m^2/C^2 * 324 C^2) / 49,000,000 m^2
Canceling out the units:
F = (8.98755 × 10^9 N * m^2 * 324) / 49,000,000
Calculating:
F ≈ 591,197.02 N
Therefore, the magnitude of the electric force between these two sets of charges is approximately 591,197.02 N.