Question

A charge Q is divided into two parts such that they repel each other with maximum force when kept certain distance apart find charges on each part

Answer 1

Answer:

The charges on each part must be equal to Q÷2 for it to be maximum.

Explanation:

Let the charge be divided into two parts such that charge on one part be x, obviously the charge on the other part must be Q-x ,  the force of repulsion acting between the particles is given by the equation

((Q-x)×x)÷d²  , where d is some distance at which the two charged particles are placed, for the force of repulsion between the particles to be maximum,  the differentiation of the force acting between the particles should be zero, differentiating the force of attraction with respect to the unknown charge x

we get

Q-2x=0

x=Q÷2

Therefore the charges on each part must be equal to Q÷2 for it to be maximum.