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Question: A total charge Q is broken in two parts \({Q_1}\)​ and \({Q_2}\) and they are placed at a distance R...

A total charge Q is broken in two parts Q1{Q_1}​ and Q2{Q_2} and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, then?

Explanation

Solution

In this question, we will use the direct expression for the electrostatic force experienced by charges placed at some distance. Further, by substituting the given values in the expression will give us the required result. Also, we will study about Newtonian force and its laws, for our better understanding.

Formula used:
F=kQ1Q2r2F = \dfrac{{k{Q_1}{Q_2}}}{{{r^2}}}

Complete step by step solution:
As we know, the electrostatic force is also known as Coulomb force. Electrostatic force is the attractive force or repulsive force between two electrically charged objects.

Here, the electrostatic force is given by:
F=kQ1Q2r2F = \dfrac{{k{Q_1}{Q_2}}}{{{r^2}}}
F∝Q1Q2F \propto {Q_1}{Q_2}

Here, we have product of Q1Q2{Q_1}{Q_2} is maximum, so we have:
Q1=Q2{Q_1} = {Q_2}
∴Q1=Q2,Q2=Q2\therefore {Q_1} = \dfrac{Q}{2},{Q_2} = \dfrac{Q}{2}

Therefore, we get the required result.

Additional information:
Force is simply any push or pull. We already know that the S.I unit of force is Newton, which is represented by N. Also, we know that the acceleration is defined as the increase in the velocity of an object. The acceleration is measured in meters per Second Square.
There are three laws of motions which are given by the physicist Newton. These three laws of motion relate an object's motion with the forces acting on the object.
Here, the first law of motion states that an object continues to be in rest or in motion in a particular direction until and unless any external force is applied on the object.
Further, according to the second law of motion, the force on an object is equal to its mass times the acceleration. Also, this law also gives us the relation between momentum and force.
Also, the third law of motion states that every action has an equal and opposite reaction.

Note:
We should remember that Newtonian force and electrostatic force are different, as Newtonian force is force experienced by classical objects and electrostatic force is force experienced by static charges having some distance between them.