Question

Three identical metallic conducting spheres carry the following charges: q1 = +7.8 μC, q2 = −1.4 μC, and q3 = −4.0 μC. The spheres that carry the charges q1 and q2 are brought into contact. Then they are separated. After that, one of those two spheres is brought into contact with the third sphere that carries the charge q3. What is the final charge on the third sphere?

Answer 1

Concepts and reason

The concepts used to solve this problem are charge on a sphere.

Initially, find the charge on each sphere when two charges ( and ) in the sphere are brought into contact.

Finally, find the final charge on third sphere when any one of these two ( and ) charges contacted with the third charge after separated and spheres.

Fundamentals

The expression when two spheres are brought into contact is,

Here, is the charge on each sphere, and are the charges in the sphere brought into contact.

After separated and , when one of those two spheres brought into contact with another sphere, again redistribution happens in charges.

The expression for final charge on the third sphere is,

Here, is the final charge, is the charge brought into contact with one of the separated charges.

The expression when two spheres are brought into contact is,

$9=9+92 $

Substitute for and for in the equation $9=9+92 $.

The expression for final charge on the third sphere is,

After contact between and the charge will be equally distributed, so the charge on becomes.

Substitute for and for in the equation .

Ans:

The final charge on third sphere is .