two charges of 40 microc and -20 micro c are placed at a certain distance apart. they are touched and kept at the same distance.the ratio of their initial to the final force between them is

say they are d = 1

F = k (4)(-2)/1^2 = -8 k attracting

later each has average (4-2)/2 = 1
in other words 10 microc each but now they repel (same charge)
F = k (1)(1)/1^2 = k

-8/+1 = -8

To determine the ratio of the initial to the final force between two charges, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's denote the initial force between the charges as F_initial and the final force as F_final. The ratio of these two forces can be calculated using the equation:

Ratio = F_initial / F_final

To proceed, we need to find the values of F_initial and F_final.

1. Initial force (F_initial):
F_initial can be calculated using Coulomb's law, which states that the force (F) between two charges (q1 and q2) separated by a distance (r) is given by:

F = (k * |q1 * q2|) / r^2

In this case, we have two charges, +40 μC and -20 μC, placed at a certain distance apart. However, we do not have the value of the distance (r). So, the initial force (F_initial) cannot be directly calculated at this stage.

2. Final force (F_final):
When the charges are touched and kept at the same distance, they will share their charges and become a single charge. Since both charges attract each other, the final force (F_final) will be the force between this single charge and its mirror image, which is twice the value of the initial charges.

F_final = (k * |2 * 40 μC * 2 * (-20 μC)|) / r^2
= (k * |1600 μC^2|) / r^2

Here, k is the electrostatic constant, which is approximately 9 × 10^9 N m^2/C^2.

Now, we have the expressions for F_initial and F_final. To find the ratio, we substitute these values into the ratio equation:

Ratio = (F_initial) / (F_final)
= (F_initial) / ((k * |1600 μC^2|) / r^2)

Since the distance (r) between the charges is not specified, we cannot determine the actual values for F_initial, F_final, or the ratio without this information.