In a thundercloud there may be an electric
charge of 47 C near the top and −47 C near
the bottom. These charges are separated by
approximately 1.8 km.
What is the magnitude of the electric force
between them? The Coulomb constant is
8.98755 × 10^9 N · m^2
/C^2
.
Answer in units of N.
To calculate the magnitude of the electric force between the charges near the top and bottom of the thundercloud, you can use Coulomb's Law, which states that the electric 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 between the charges,
k is the Coulomb constant (8.98755 × 10^9 N · m^2 / C^2),
q1 and q2 are the magnitudes of the charges (in this case, 47 C and -47 C),
and r is the distance between the charges (in this case, 1.8 km or 1800 m).
Plugging in the values into the formula:
F = (8.98755 × 10^9 N · m^2 / C^2) * (|47 C * (-47 C)|) / (1800 m)^2
Calculating the magnitude of the charges:
|47 C * (-47 C)| = 47 C * 47 C = 2209 C^2
Calculating the distance squared:
(1800 m)^2 = 3240000 m^2
Substituting these values into the equation:
F = (8.98755 × 10^9 N · m^2 / C^2) * (2209 C^2) / (3240000 m^2)
Simplifying:
F = (8.98755 × 10^9 N · m^2 * 2209 C^2) / (3240000 m^2)
F = 15,374.23125 N
Therefore, the magnitude of the electric force between the charges is approximately 15,374.23125 N.