Calculating Maximum and Minimum Force Between Point Charges

To calculate the maximum and minimum force between point charges, we need to first distribute the charges as two point charges separated by a fixed distance. Let's assume that we have N fundamental charges, each of charge q, and we want to distribute them evenly as two point charges separated by a distance d.

- Determine the Charge on Each Point Charge

To distribute the charges evenly, we need to calculate the charge on each point charge. Since we have N charges of charge q, we can divide them into two equal groups of N/2 charges each. The charge on each point charge is then q(N/2).

- Calculate the Distance between the Point Charges

Since the charges are distributed as two point charges separated by a fixed distance, we need to calculate the distance between the point charges. Since we want to distribute the charges evenly, we can divide the total distance between the point charges (d) by the number of pairs of charges (N/2 - 1). This gives us a distance of d/(N/2 - 1) between each pair of charges.

- Calculate the Force between Two Point Charges

The force between two point charges can be calculated using Coulomb's Law:

F = k(q1q2)/r^2

where k is Coulomb's constant, q1 and q2 are the charges on the two point charges, and r is the distance between the two point charges.

- Determine the Maximum and Minimum Force

To determine the maximum and minimum force between the point charges, we need to calculate the force between each pair of charges and find the maximum and minimum values.

The maximum force occurs when the point charges are closest together, so we can calculate the maximum force by using the minimum distance between the point charges (d/(N/2 - 1)) in Coulomb's Law.

The minimum force occurs when the point charges are farthest apart, so we can calculate the minimum force by using the maximum distance between the point charges (d) in Coulomb's Law.

- Calculate the Ratio of Maximum to Minimum Force

To calculate the ratio of maximum to minimum force, we simply divide the maximum force by the minimum force:

Ratio = (kq^2(N/2)^2)/(d^2(N/2 - 1)^2) / (kq^2(N/2)^2)/d^2

Simplifying this expression gives us:

Ratio = N^2 / 4(N-1)

Therefore, the ratio of maximum to minimum force between N fundamental charges each of charge q distributed as two point charges separated by a fixed distance is N^2 / 4(N-1).