Question

Two 4.0 kg masses are 2.0 m apart on a frictionless table. Each has 1.0 μC of charge. What is the magnitude of the electric force on one of the masses?

Answer 1

The magnitude of the electric force on one of the masses is approximately 2.24875 × 10^-4 N.

Step-by-step explanation:

The electric force between two charges can be calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this case, the two charges are 1.0 μC each and the distance between them is 2.0 m. We can calculate the magnitude of the electric force as follows:

1. Convert the charges to coulombs: 1.0 μC = 1.0 × 10^-6 C.
2. Use Coulomb's Law: F = k * (q1 * q2) / r^2, where F is the force, k is a constant (8.99 × 10^9 N·m^2/C^2), q1 and q2 are the charges, and r is the distance.
3. Substitute the values into the formula: F = (8.99 × 10^9 N·m^2/C^2) * [(1.0 × 10^-6 C) * (1.0 × 10^-6 C)] / (2.0 m)^2.
4. Calculate the magnitude of the electric force: F = (8.99 × 10^9 N·m^2/C^2) * (1.0 × 10^-12 C^2) / 4.0 m^2 = 2.24875 × 10^-4 Newtons.

Therefore, the magnitude of the electric force on one of the masses is approximately 2.24875 × 10^-4 N.