<h2>20. How much charge is on sphere B after A and B touch and are separated?</h2><h3>Answer:</h3>

<h3>Explanation:</h3>
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:

<h2>21. How much charge ends up on sphere C?</h2><h3>Answer:</h3>

<h3>Explanation:</h3>
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:

<h2>
22. What is the total charge on the three spheres before they are allowed to touch each other.</h2><h3>Answer:</h3>

<h3>Explanation:</h3>
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:
