Coulomb's Law states that the force between two charged objects is:
* Directly proportional to the product of the charges
* Inversely proportional to the square of the distance between their centers
Let's break down the problem:
1. Initial Force: You're given an initial force of 12 Newtons at a distance of 4 meters.
2. Reduced Distance: You need to find the new force when the distance is reduced, but you haven't specified how much it's reduced. Let's say we reduce the distance to 'd' meters.
Calculating the New Force:
* Initial Scenario: Let the charges of the two bodies be q1 and q2. We can write the initial force as:
F₁ = k * (q1 * q2) / 4² (where k is Coulomb's constant)
* Reduced Distance Scenario: The new force at the reduced distance 'd' would be:
F₂ = k * (q1 * q2) / d²
Finding the Relationship:
To find the new force, we need to figure out the ratio between the initial force and the new force:
* F₂ / F₁ = [k * (q1 * q2) / d²] / [k * (q1 * q2) / 4²]
* F₂ / F₁ = (4²) / (d²)
* F₂ = F₁ * (4²/d²)
Example:
Let's say you reduce the distance to 2 meters (half the original distance). Then:
* F₂ = 12 Newtons * (4²/2²) = 12 Newtons * 4 = 48 Newtons
Conclusion:
The force between the charged bodies will increase as the distance between them decreases. The new force will be directly proportional to the square of the ratio of the initial distance to the new distance.
