Two charged bodies exert a force of 0.225 N on each other. If they are moved so that they are one-third as far apart, what force is exerted?
To find the force exerted when the charged bodies are moved closer together, you can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / d^2
where:
F = force between the charged objects
k = Coulomb's constant (approximately equal to 9 x 10^9 N m^2/C^2)
q1, q2 = charges of the objects
d = distance between the objects
Let's say the original distance between the charged bodies is d. According to the problem, the original force between them is 0.225 N. Now, when the bodies are moved one-third as far apart, the new distance between them becomes d/3.
To find the new force, we need to compare the original and new distances. We know that the force is inversely proportional to the square of the distance, so we can set up the following equation:
F1 / F2 = (d2 / d1)^2
where:
F1 = original force
F2 = new force
d1 = original distance
d2 = new distance
Substituting the given values into the equation, we have:
0.225 / F2 = ((d / 3) / d)^2
Simplifying, we get:
0.225 / F2 = (1/3)^2
0.225 / F2 = 1/9
Cross-multiplying:
F2 = 0.225 * 9
F2 = 2.025 N
Therefore, when the charged bodies are moved one-third as far apart, the force exerted between them is 2.025 N.