Question

Two identical small conducting spheres, having charges of opposite sign, attract each other with a force of 0.108N when separated by 0.5m. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of 0.036N. The initial charges of the spheres are.

Answer 1

Hint: In this question, we will use the basic equation for the electrostatic force experienced by the two charges at some distance. Further, by substituting the given values in the equation will help us to get the required result. Also, we will study the basics of force and electric field, for our better understanding.

Formula use:
$F = \dfrac{{k{q_1}{q_2}}}{{{r^2}}}$

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
$F = \dfrac{{k{q_1}{q_2}}}{{{r^2}}}$

Now, when we substitute the given values in the above equation of force, we get:
$F = \dfrac{{9 \times {{10}^9} \times {q_1} \times {q_2}}}{{0.25}} = - 0.108$
$ \Rightarrow {q_1} \times {q_2} = - 3 \times {10^{ - 12}}$

Now on connecting these two charges, since the two charges are identical so they will have equal charges.

So, the final charge will be given as:
$\dfrac{{{q_1} + {q_2}}}{2}$

So, the final force will be given as:
$F = \dfrac{{9 \times {{10}^9} \times {{({q_1} + {q_2})}^2}}}{{4 \times 0.25}} = 0.036$
$ \Rightarrow {q_1} + {q_2} = \pm 2 \times {10^{ - 6}}$
$\eqalign{& \Rightarrow {q_2} = \pm 1 \times {10^{ - 6}}C \cr
  & \therefore {q_1} = \mp 3 \times {10^{ - 6}}C \cr} $

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

Here, the electrostatic force is given by
$F = \dfrac{{k{q_1}{q_2}}}{{{r^2}}}$

Here, we know that the S.I unit of force is Newton, which is represented by N.
Also, the electric field is defined as the electric force per unit charge:
  $E \propto \dfrac{F}{q}$
Here, F is force experienced by the object and q is the charge on the object. So, we can say that when the electric field at a given point is known to us and force is also known, then we can get the charge or if the charge is known to us we can get the force experienced by the point charge.

Also we know, time is defined by its measurement. Time is what a clock reads. The S.I unit of time is second.

Note:
We should remember the difference between the electrostatic force and mechanical force, as electrostatic force is the force experienced by point charges at some distance whereas, mechanical force is the force experienced by a classical body having mass and some acceleration.