How does the electric force between two charged particles change if the distance between them is increased by a factor of 3?
A. It is increased by a factor of 3.
B. It is increased by a factor of 9.
C. It is reduced by a factor of 9.
D. It is reduced by a factor of 3.
Answer (1)
The electric force between two charged particles is inversely proportional to the square of the distance between them.
When the distance is increased by a factor of 3, the new distance becomes 3 r .
The new force is proportional to ( 3 r ) 2 1 = 9 r 2 1 , which is 9 1 of the original force.
Therefore, the electric force is reduced by a factor of 9: C .
Explanation
Problem Analysis Let's analyze the problem. We are given that the distance between two charged particles is increased by a factor of 3. We need to determine how the electric force between them changes.
Coulomb's Law The electric force between two charged particles is described by Coulomb's Law: F = k r 2 q 1 q 2 , where:
F is the electric force,
k is Coulomb's constant,
q 1 and q 2 are the magnitudes of the charges,
r is the distance between the charges.
Initial Force Let r 1 be the initial distance between the charges, and F 1 be the initial electric force. Then, F 1 = k r 1 2 q 1 q 2 .
New Force The distance is increased by a factor of 3, so the new distance r 2 is 3 r 1 . The new electric force F 2 is: F 2 = k r 2 2 q 1 q 2 = k ( 3 r 1 ) 2 q 1 q 2 = k 9 r 1 2 q 1 q 2 .
Force Ratio Now, let's find the ratio between the new force F 2 and the initial force F 1 : F 1 F 2 = k r 1 2 q 1 q 2 k 9 r 1 2 q 1 q 2 = 9 1 . This means that F 2 = 9 1 F 1 .
Conclusion Therefore, when the distance between the charged particles is increased by a factor of 3, the electric force is reduced by a factor of 9.
Examples
Imagine you're adjusting the distance between two magnets. If you triple the distance, the magnetic force (similar to electric force) decreases significantly, becoming nine times weaker. This principle is crucial in designing electronic devices, understanding how signals weaken over distance, and optimizing the placement of components to minimize interference. By understanding the inverse square relationship, engineers can effectively manage and control forces in various applications.
