We'll solve this problem by using the concept of electric potential or simply called potential , which is <em>the energy per unit charge, </em>so the potential
at any point in an electric field with a test charge
at that point is:
The potential due to a single point charge q is:
Where is an electric constant,
is value of point charge and
is the distance from point charge to where potential is measured. Since, the three spheres A, B and C are identical, they have the same radius
. Before the sphere A and B touches we have:
When they touches each other the potential is the same, so:
From the principle of conservation of charge <em>the algebraic sum of all the electric charges in any closed system is constant. </em>So:
Therefore:
So after A and B touch and are separated the charge on sphere B is:
First: A and B touches and are separated, so the charges are:
Second: C is then touched to sphere A and separated from it.
Third: C is to sphere B and separated from it
So we need to calculate the charge that ends up on sphere C at the third step, so we also need to calculate step second. Therefore, from the second step:
Here and C carries no net charge or
. Also,
Applying the same concept as the previous problem when sphere touches we have:
For the principle of conservation of charge:
Finally, from the third step:
Here . Also,
When sphere touches we have:
For the principle of conservation of charge:
So the charge that ends up on sphere C is:
Before they are allowed to touch each other we have that:
Therefore, for the principle of conservation of charge <em>the algebraic sum of all the electric charges in any closed system is constant, </em>then this can be expressed as:
Lastly, the total charge on the three spheres before they are allowed to touch each other is: