When a charged body is divided into two equal parts, each part will have a charge of Q/2. Let us assume that these two charged bodies are placed at a distance d from each other. The force between them can be calculated using Coulomb's law.



Coulomb's law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The mathematical expression for Coulomb's law is given by:

F = k * Q1 * Q2 / d^2

where, F is the force between the two charges, Q1 and Q2 are the charges of the two bodies, d is the distance between them, and k is the Coulomb's constant.



If we substitute Q1 = Q/2 and Q2 = Q/2 in the above equation, we get:

F = k * (Q/2) * (Q/2) / d^2

F = k * Q^2 / (4 * d^2)

We can see that the force is directly proportional to the square of the charge Q and inversely proportional to the square of the distance between the two bodies.



To find the maximum force between the two bodies, we need to differentiate the above equation with respect to Q and equate it to zero.

dF/dQ = 2 * k * Q / (4 * d^2) = 0

This implies that Q = 0, which is not possible. Therefore, the maximum force occurs when dF/dQ = 0, i.e., when the charge on one body is twice that of the other.

Q1/Q2 = 2

Substituting Q1 = 2Q2 in the above equation, we get:

F = k * Q1 * Q2 / d^2

F = k * (2Q2) * Q2 / d^2

F = 4 * k * Q2^2 / d^2

We can see that the force is directly proportional to the square of the charge Q2 and inversely proportional to the square of the distance between the two bodies.

Therefore, the force between the two charged bodies is maximum when the charge on one body is twice that of the other.